%!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: sep-03.dvi %%CreationDate: Tue Sep 09 18:56:27 2003 %%Pages: 22 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR10 CMSS10 CMTT10 CMR17 CMSS17 CMR8 CMBX10 %%+ CMR6 CMR9 CMSS9 CMMI9 CMTI10 CMMI10 CMMI8 CMSY10 MSBM10 CMTI9 CMSS8 %%+ MSAM10 CMMI6 CMSY8 CMSY9 CMSY6 CMEX10 CMCSC10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips sep-03 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.09.09:1856 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /P put dup 101 /e put dup 105 /i put dup 109 /m put dup 114 /r put dup 115 /s put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 12 /vextendsingle put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS8 %!PS-AdobeFont-1.1: CMSS8 1.0 %%CreationDate: 1991 Aug 20 17:34:12 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 69 /E put dup 80 /P put dup 88 /X put readonly def /FontBBox{-65 -250 1062 761}readonly def /UniqueID 5000801 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B17498276F99362748F6E97327D 7CDA3F577075245561191667923D37830EEC37A0161B6A3EC8FDD63CDB8C8D4A AD39C69A264813FA79C25E85AC95C71AB965F6C14A4A1ACF5BAE27A5F628B172 47CF6A12008558438874199C237501B72BFEFE64B606A327623BD8B217E8349B 7BF5C2204F4DE2FB269845D5714A31151A66064419CCC46A63F8E54B92B5070F F3D80801DBEC658CD3926B15BE3D4B7591FC36663D3C03926D0D3637B53BCC22 73C8E0001B416A65FC67C53383458DC125FD14FFE391BBBA321B5AF5DEF85DBA 5A5FD759FD2AAB6AF31CDA6202EBB763E3CAC1FF91B1175EF818FD662B60C642 738A3B4F27822A0560BB7C08AD42F976351FA5225A0E6D56C7FBE06A809CC468 FB2E90C84FA56C62CB7BBFC80BD94F5C6BC0EED14433A4A356D2D15DC87B34B0 99A100502F55A32D736757642F9F9719FD9E35A1430A72C254614B4000113705 5474FCFCE47A6978F69FA467B818309E61598EC18089BB924C393B3FF1280D72 E1969BF5AD3D1074FF13202D4CC324396BAFF2397DAB2C516C656B6B240F023D 0C28AEBB957C23012C971D444DD1C4C2BD7DCE178D46CF8EC20DCAB9A930907E 124F3B3B8D16DBF166BA40CD780DE2155BF21EC2C3E0073422E54A09DF4A9491 63B55882122F6B40490D81533CB0E16967E32D4F5B5D5D14F578BAA0137704A3 2386E6AA4E3D160559EB245625253380CE64C30B41B573D7249B0B6157B02EFE 0D82006B4CF4A294FDDAB5B87CAD0B2D3367F9138EE0922FBDD3D7BFE4C6B297 762F95616A75D0FC2D2E22D79172DF1A3287C67BD27658A448FC61077B3033AA 5479ABBF5CD952B5E19E437CD642CDC43FBB26115DCC019FEB3195F08AB66435 26F1BA44091673778244CB347678767ADE42D06CD448C4DFAF34A02517FF3520 846DB86F281BBCBE56CABC04705B37D048A0A9A6DE6F8BD6A55D40307BB47EDC EEAFCD4ADF74BF440311303D89B63D53833064B2C21C1A7543B58C554BC4A104 CC20CB0B291211DF95DE9073B2DC2A03C7CBB5098773692B72DD5FFCD29FFDF0 5CD174ED168CF4C6741538080C6308C7A24A9F5C0E502DC155FCBB108272E9C8 E6648447DA92F1A4BE087D7105D2E48EC8FB46D486E31C97E872C33990EC9782 18652B526CEA150961AA1189CD023D93A06AABC6F35C1ACEC81D841F3AC7B2E2 3EE357002230A23984184EA25D14ABFD686D39904901C53D7B60C6623FBCAB3F 01A2BBE53A4CCBF793F5FEC394499C552AABDA3A8AA044E2666A88A7EF22B5F0 6A4E77D8057CC5D313ABEE0D5BAB26A8164BBA799112EF815A2393F4ECAC1A17 FAE87DA2ADC5DA5283FD6C9D153366A6B4B7A1871486C2A39BD680C048EBC211 C30AE5D8080D70F8A9FF34DC593D17A95A63B621D2D3EA73C9E71454B2382A5A 5E3DF8039849F3BB71E8C3969AA5D55373B8B67364DBD978799B5A1CF0A41041 F3A8F29BAB2B4B3C1B0EFCCFAD88E705924F1763CBF00845C0464CC0FEC2C601 7DB8F07A6159AF6004CB2F4D851E912509341BEED641A3FCBC9B104DA6831DB6 730B4659C60F4638E4365BD0A495F91C506931EC1BF90F4C1699E5C49BDB9110 5591AD01B9294F1DF91DC87987C46606D8DBC6C1BE20D7546175767D7A44B2D2 67461DCB33A9F49714FE3B69A9B6A7DCF9E85D29F0796F513156D9ADB9C222BF C0FE2E386AEC2698E8E392 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 21 /greaterequal put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 50 /element put dup 54 /negationslash put dup 102 /braceleft put dup 103 /braceright put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 21 /greaterequal put dup 79 /O put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 79 /O put dup 99 /c put dup 110 /n put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 15 /satisfies put dup 113 /rightanglene put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 58 /colon put dup 65 /A put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 65 /A put dup 67 /C put dup 69 /E put dup 70 /F put dup 71 /G put dup 73 /I put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 AEBE70DAAED49EA45AF94F081934AA47894A370D698ABABDA4215500B190AF26 7FCFB7DDA2BC68605A4EF61ECCA3D61C684B47FFB5887A3BEDE0B4D30E8EBABF 20980C23312618EB0EAF289B2924FF4A334B85D98FD68545FDADB47F991E7390 B10EE86A46A5AF8866C010225024D5E5862D49DEB5D8ECCB95D94283C50A363D 68A49071445610F03CE3600945118A6BC0B3AA4593104E727261C68C4A47F809 D77E4CF27B3681F6B6F3AC498E45361BF9E01FAF5527F5E3CC790D3084674B3E 26296F3E03321B5C555D2458578A89E72D3166A3C5D740B3ABB127CF420C316D F957873DA04CF0DB25A73574A4DE2E4F2D5D4E8E0B430654CF7F341A1BDB3E26 77C194764EAD58C585F49EF10843FE020F9FDFD9008D660DE50B9BD7A2A87299 BC319E66D781101BB956E30643A19B93C8967E1AE4719F300BFE5866F0D6DA5E C55E171A24D3B707EFA325D47F473764E99BC8B1108D815CF2ACADFA6C4663E8 30855D673CE98AB78F5F829F7FA226AB57F07B3E7D4E7CE30ED3B7EB0D3035C5 148DA8D9FA34483414FDA8E3DC9E6C479E3EEE9A11A0547FC9085FA4631AD19C E936E0598E3197207FA7BB6E55CFD5EF72AEC12D9A9675241C7A71316B2E148D E2A1732B3627109EA446CB320EBBE2E78281CDF0890E2E72B6711335857F1E23 337C75E729701E93D5BEC0630CDC7F4E957233EC09F917E5CA703C7E93841598 0E73843FC6619DE017C8473A6D1B2BE5142DEBA285B98FA1CC5E64D2ADB981E6 472971848451A245DDF6AA3B8225E9AC8E4630B0FF32D679EC27ACAD85C6394E A6F71023B660EE883D8B676837E9EBA4E42BA8F365433A900F1DC3A9F0E88A26 32696950409CA08F623B079769D877EC7F8D3FF526CF464F07C3406CC8CD11C3 18CC7166C5E3906D980E8E2979B4B906586844F4E5C0E0D9C80073174E6A906F 4E700350FFE41113F22B3D158018D91CDC65AAC1E0E6F3235D1874BA99710412 14AF1219586F1EEBC99FEF2F169CD4ADF43581F657C863DAAB7F08A9C9CCCF3D E67700D4A7B591FC36B36F990DEA9DD95D36B1FA3A2A2B3F89A6CABFF8549540 76077B750F2C7C20BE8EB57B670294D36C324516D226BA05F9C36A5A8BE77CD8 2E4E9479BAE394DEEC13116865F253D531DD80BF1B26D112855893B2A61639F3 43053D71930F6EF88DAFF54B2C2D7F85D3D375476561E03330452A13CED73168 A20DC4CBC150EED68FC11A1B4FCF6406B92783EAA1B9790A4C33F69BBA976B2C 1B277367E75F3E84D8E0C6CFAABCD074553464149F0149E02559437F653CB655 EB6460FAF75222D41F0961EC975C04204549338A1F94E0E83A41DAE898F540DD F2BC57CA0BF50AE4EE90F39BD4F4C8CD9723AC5A8F1E34D02263611A484B0538 33CACF85098BD60D81A821270C074D76A3552C404ECEE8E79E2498A394EF5F3A 64024B583D8C613A01A5A2607EB4042ED858EC4721987908C674293E3AA5A7B9 0A6249BF654A3E0FCA2749D320E2FE59AF6C22F616A91B168E5141DAC42AA302 EC69D4290E28D7C880A7ED2C8C9E3F46512974F067AA6A9DBCC6E7808FCDB17A 94935C87523BFE6E3BAC15CD7D037D39BE8EDA9ACC49F37D4494CDE107D040F3 85DD765C4F43EFE62805C9955474F047E84858C26DDDEFA7EF86152AD816856D 2873B128FACD9EE0C8721B6E10CC8A985D7902D6EE4448444FCA23917B7ADD18 18A53A386858C2084CBA66CC26E9C5C82BBCC5D2776C6EC4FDDFCF3963B24882 1A4A30E49D619A91BA4370AFFE59B5952AC632BC448EEA8E0922FA4A184F8B65 326C76B3D86F9A9B12E1268ADBF946FACE466126AE2A069EBBA36CEE9A6E4DA1 D44EC568E1C47BCCC7D0049656ED695D829920C6B7D6531DBCF8FAE94A410711 B1C555D66633B9DB779C0DBC93F8F95F50D0820E48E2E9F668144A38D2ACFA5D F8F216EE2DE7E8EEC8980855A03BB34CEA5F4B308487F208A596E83443078456 C834B539C9B17D4B6FDEBC05A592650F3C987259629C43A540FBD2F57C26284C 006E0E0232CA1AD44DF1C6803541B36D9726AB3E1DD1DF1CC543FBEC25DFF07F 172B1C70FAA02B21890781C99EA0123C8E1373B7CDD8236B65CA9262122A45C0 EE111970CC764E077BF6BFF0C8D061E3DD8D08E1A40AEA3B26E0D8D0A2497A5D 8CDB9170EAC8E62B6C880DC7F5355BEB5E6E1E2D2229AF16A9CD089D4AE12A9A 4C873266AB7D3C4967109C169D50FB1EF67D6B49F643EB3DBDD14315411EE935 BA4005F5573FAF1DB8D8DA88513FA6008E296FB573939E93618401C5BC0B52B3 929721169148E1D315FB082D333F936D539E7E13DF08A87022DB7114EE5B03A9 F029377E1EE40ACF63A0CE5782E6F70752AA839352C6D6D2FA1DBEF34CDF592E 5175EADB6EB0DA131444B80713BCE5166DC976FE19D50A7C2E3B7D22643A2ABB E2D522D5AA7C5A334E62CA87E9DBE64705211458BC70C90D3E5A59D860D65F38 E6EF35030BD3A48D74048909A463D60F9E8B54D30015F36C95CAC8C189452F14 CF0194A6041161556253A4B6E83A191CE8A1A20269D970C8080F3A637CFB8E1B 259088BB65D86C7B065B8EDCAF0731DABF5371E783F1D4B5640043273D0ADF02 64100340DC6998484055F0A8FDD172667C91728983065D4F03105569E09EB506 C2B0D6C66F554DA398ADAB980369C3C67581F18510DF6DDEE260D8DCB17E044A 15143268198A4BBD4A2FF4E1314E2A12837CD46949C1903E21E4A1D0681D853A EF9F430B1FC2315A2241B33C4BBCBA5C5708473C1F7FBB0C7DFE7B610FDE5C94 1D8F4929E88704C248E31C4A45FE3E1E70178FC04E3F7F85E5763C16AEDB9EBF 6CA2B2F50E79B64FCEA0CD9B9EB37D2AC26A62EDC803C4996A51303544A96742 F9979AE6D65F0299A91BA8EC5FFFF51658465E2D8630E00A39049F7BA25D4D0F E80B95F8DEB318606103C540402D42B2D33B4340C9C0EF5ECD55D338FE75A9F7 8B00A71C51D6731635452B82617178B42182E473DEF074ED769916DADB792220 0198F036871D7B6FF1A4898BAF2F4DE77EBCF9671D58FE781022FD0AEAD854E1 0362789B319C38B8A93FD72F0B718D3BC714563E4DBB2B3F46ABC0541D742CCD EDB5BB00DADD48B6E3C3455F9F7ED3A655198FFAD886DE015D1F812C77FFD5A3 C50CEDDB4C5DE2E561559AC32BA779B5CF9E8B0449A8AB74B2EB968A302B1346 5B57B80A696E6BED3EF21817FE450DB69E0E2BAE28EA050AF29C2A03422F296D 3DE3912066BA48C7BFBC67553F62D9BC9B5461D180BF763C156FAF229CBD218A E45A12CB82A0A7BF1DB51C4C5BC9A960D1299FC087BA3E4BB001011872B4B36D B96CA40DB937D3987A5B68D65B3F49E89D730273E0562244DF9CF832C120323A 4B30212787F2471A5905E726FC8B7AB19CDB7E58232385B42520579923C1A632 C78BEAD61C78F716CADBDC07B2FB69FD50DC7AC711865F6E575A252AEAB67A5D 8E8BB835BDED8B334AE2E2327543C620CB772B8479ECCE6DD7FFCF0DF9A00B87 2143AD1D45AD672A3899608F75FC8792D3F2EA240F477C96794AC96EE30EAC93 E44A80EB361A6E8E0777612BF54D417D10845CB0DF60D864BCCEFCF003AFFD31 F72D8DC8031FD3B7A928AE283C8F74FC73C04BB574B33FB656C5E6F57636CD27 1B1F377836097C2EE67011844ADB2958BD085085D8DB25220F4AF8866FA9F849 451FB5243D6789C6626CD388A215200036CE911A2138ED56DF36D9CCA1301681 D4CC262CB20ED12C3C19D4217A4A38406014E8FAB68395153D9FA52A48D8719E 5BF7F43B87D4C1C7332F11AA37ADA80F1B2713ABEDF90A973B49DC3727DED789 C88873E68A56F5FEC42238D58A950B5EBA3A0E691F50B2819E63289A3F65D89B 18EAAC05CF68E1C2C1AFDA397FA8343ECE9A3792F951D7CB94CD5BFBA2D25C43 ADC63D2A9F635488165DBD1322E6FC534C4CF6761B12D706A31F7ECD992E1BD4 95806651C61B72CBBE28E55EE53B62DE2C1E8FD1632B00B58DF1A988FA9DDF37 E73D03973FE6426197FBA388A70A4C8E9EAC7AF09916259AFA2A253CFD869A3A BC53C2147B7F5124C4CA6064C3754F7F2A1FD06FAEF371119AB4124717DB5485 055FB1C918A5DB35742A2A6AB470D4A71FC2D7A953AA913F3EEE8473DFE878DF AC39BE51F3FCA9F681BB19E3AA65A29C18B7F21A6BDF28167FFB626AD476B5BC 067C3BFCBFB9CB6B1D0620D1D216445F4061D75531E342BE466930A672BB0F34 3108008B07D7AC41E06CF483C3407B8EDF107E2CEA998BAED8CEAC5662C1A05C DBB3A3BB2891CC04400F5CD3FCFBEC4DE8B2AA4163C0D7D2233F091E0D21597D 84DD43863D656FABAA05D585E8B6677CA19AE71ECCABE8700BC6E20B0C2206FF 99A56E638F885AE30668599623B797DE18C2969E75DF6AC630756ACB95739258 75B7FF19C34FF3A35F8E53E8F05B1210B9AC4D1245EFE5DAF4D6A82AD45E87A4 AED38CDCD4EF3C7BE0FF7E54D08385E822E384B3701033FCD23AB28DFC1AF51A 30C7CDA24689E0FB446FEE3D14C42104090A8B1959D8DD495E58544B2C477DB1 308E305D06E2EAFC2012C1E2442BEF31580BB60BF443F4D61AEF500C9A329E99 1A8F1519CAFCB484F1EAC61CD24757C5F21A382059784CCB7111CD41F80F3ACA 3DC416E6564C26484E39C19ABD51ACAC8ED4DC63F5E893B9FD51D97D824CD4E7 7AC199A89112B3FE7AD0376A03BDBC8C8E09CFAFCF9BEDCF75C885894D18FBD1 491669E5ABE52CF1E3571244A852FBA657378F62B83E0F365F42D34B3FBDD86D 92B2C19B0F5810DD65F8ADE192371FAF1170BF41A938EF49B6C5C4858387D0B4 2456D6D7542BD6184AE45295E28ADB9AD947F33F551895FCBDCD3B7E3DD3C995 2C88B20CCB2EFD94A0D1E7E239B28407D087271E3215D2027CC8137CC6107320 4E1ADB5BA8D84D20E636753DD1D8F1F043FCCD6BF0D876B90FA508A8B342F61C CBFE18D8E25E3B9F9D316E3BB6DD53205DE936E2EA10FB26D7E7E787B8E39889 4C3EF1AC3F4760987B8B59C7FBCC39E80BE0315C0A96BEC9029D330F928B75BF C875C401AAF6B4F1E7B1AAA55BDE58F555F81504C262C4ED1D65EEA32B22A876 A4BB57338ACC834C5DFC1B40D30D9CBE466875FB44C7DDE0CCCB7898F1190BAA 3E4A39DD2149245154529DA6EFCE1C683CB6E0FFA0AA9669CD3E6AE872A3F81C 0EDAB93C0A60EC88D903F73B8E2C30DDC73363E642AE1F96F2E02E45284FA3B1 BF77E865A214720D99059946A5E99DACB5F77ECA5AB51EDFDC7122A039A78502 6B1B80948BFE087330557E96B409FB9A9EFB723CE23035D0CB2DB908EA64DB68 F0FCB4A1848616C47E9CD4BA4809886920D422B883F556E844AE1A9BEBDB28FA 6C8BB35C63E7AD58361776A5F391B32B641C30AB61B94B5F4783C9836C76D8FA 38127D59684BAE8F23DAF6D3FD739BFBDC47FB45EC6082BFC5F0308467D3FE1A D2AB6AD92651C3A7CAB62EA74CDC586254EBDF08D73A74AE12F30D974E369A35 CD4889A0947A7537AA44296CF8E008C52BEA65EBD2C9AED94BBD12E0DBF2F38B E8E540C6006AB30D15333F1E1A6DFBD1640D09F5A6963DFA50A7AA05BEC91533 C1A0094AB4F570C0B3F8AD2DFE0C1DE4C3CE9695DC6A5628A8793A9F674E4FEE A373996D674AA3E90309E55CC98D5EB67EEEF9E4BBA89589F70CCC06A205C72B E72B3B50FF177C1BA5369DF2B206F31A15192F71073DB3108BFC0723939C3D36 986B870089FCCF714F80691B4759CC37F8858F1A165A23740093C9F4954DD269 0D89BD26CF6F46FFA5A03BED911A60891F847DA2AAEC972A58C0852A42543532 4C903133D19FBA3933ADD2A8CDE5BF8F38CF8183827107667EC84527779AC098 E257FE4B6F6E611D80F8EC6B48E4FAE004A9661705135EF259FCC62B7F9836C4 A404AAD2D0C54AAED643CCA7B182255DA9F50CE9560E9EF6BD7F63E07C0B5BDA E23761FAB95F2D7CE5F221863CAD79436911ED81343954B6FE561358E42F7DD2 EA639C49A6C1CD829B773A1E84FC7EDDE941657F164AA20B975BA12E82470314 458CCFE087E487F13348A511D12FCDA198E2D11B4FC3CC060D445C91F3B76407 784149700756FA9759019553317F007E4E5CD62CE10291F0199AF8FD2C6159BB 8C4C1B1DC7DBA7561533C4575573CC107BE07F16CEE828D1DECA9757A5F00BFD A942BFCFF84C3C4322FFE5688FCA0C824D83580CE38C6FF5663D0020BBBC8EDD 55BD442E78E1378B91E8ADC4D234DC2FBA939C6FB665BDA0667C022231164A09 780BD05F9A55539FE093E295A8FF42CC974EBA763ABE4D0FBC39F572EBD8AC4A 5DF34E426EC47B0319DB5AC0BA73AD3D9BCCD21EE69A5476CE7683CCB29B90FB E19C861FF695536F6D985DDA7AB36A07C378D0DDD94DFEF39AC24489363CD689 783865ADAAA51A0C501CD9C4DD3230F68A4AF0686A31375B89937447E9CA98BC EE3C53595DEEEDF0756FE434080E02CB8A824900F6FA12C6740F1FD506295C21 AED0E94BE966AA5AC164D1B022E62A349009756DBE6B3F56B8638E7A33CF7E9D B12B8E3E2389C8AC029A207E44F3A6F7E77BD61C8F86DE68AFEC20F1658DE665 9D64E07B3D370F561F787A6F1A411F68847240D77A29B10FC4F40F513E0BBB15 DA0528F0120DAE53FE012B24F99D2181FEA527A96CAF30BF16B3811B36905A33 C047003A080C13519A23F20A208E64F61FE232C92FC689E3050F3B98D8B87DC8 00B1EA0886AE4316ECEDA7269F6F3D6DD71F8AFEF897AF4399E91B75E66590F7 93C28BC91F639ADF276FCFFC38D4B196E2600A1273DA1737AD75F1BC940D40F0 58337430C7DB16F48625F5DF7065D1BF435A5FCDD6F8615110EFB1E3D2619DC0 02804BF777D4934BE6DE82F7DDAF53931FFEFCDCA2142EE05382E6A38708ACB5 23C906D39DFB582DF94D3182942B1367E228B424B19A0A6D1802EC3DCD339629 EA4ABCABFDB47549E49A30A0D3723451909C8C7C8346E60C74B0B5270C373708 C4708AFCBA0F5944336095A49F993D7BE7C52E0E90FABF51D9CFB8E6E65EA5AD 27E9BDC7BB51AE06E562F8850C123B726F4A125A3F283D16354AD895F2BA7E0C E6B8A64F8FB80C2A8AC8141AC3973E63D3769ADAE6E3920AB06888A6BB14DD7C DBA4223A9CA1EF6CEA5729DA0BBBED53D2D2BB9B505BDEEE46F6DC36095A583D D9F8302B422D14231E992B8661745B2D3E7213A0A0F975040E30F92D35D52B1D 3026D1AEADF57E68B93C06009B560FF36E0F4B414021E6A60A174EBECCA18718 95559AEEA8AF54B55F39D7968D1B15B5F3B1E6ADC71466AB433E7E0249918279 27939C0A5E3BC52D3F96A7C576A9DB313FBBB9833037C0A84178C06DBA1BED06 442E3BC8143E7FFFE2DAE15E25663B01DEE8024A3254FB2E6A7AF1384E83A0AF 226C2D8E5D0E74FD36BFCFD98E7A17C455631C8D77BD6F47A24CE7481C10BCF7 3392D70F67BB94AB84C228D625EE00D2C3E652F44A6E90786C5F5A33A0FD5A37 21137E526D03E7736016B8C34638AA0153487630397A7E6CE78073EAA4E3040D 0F6B316BA25EB9E0CF4D9F1D84752AD5A816F5BD600B46DDD7E9320D2542EC4C EDA29866EAE35901AF1AF22D0F65146995BC2687D7FCDAC660C160487431E1C7 A7E36CC2C0A3D96DAADD4707E9B6264CF1CFFDF7F3AEE364DDF9A13E8ED255F3 AA1BB1CE4462EDE018FFFCDC5675A62A474424D2201CC62B93CDA3FBFC2A50C1 6EA92788476D2C210EB77EEA4DF4FCEB77F33C94CDC87C299194C17D130B5BE6 95D49B4944F55D00D69E9EFD3E3A85C91BBB7879C431083455BCD67F43DE21E9 43BDD3F9EE9E6AE1AC4D1E643C2E002F5FE0B87F36126AA5895E70EF2BD5D557 709C117593184EA92079B1B8778D568A26FA40294A1F9EE407F8A45FAD158A8D B8355E1549B87FF84C8C26364536424CDC91692F38BD51FE0AA606DCDE2DB600 1DAC6E8EC6B437332248559E6BCF6D4B5007BA14C5BAB3DF0C521CF0BD59C63D D6CCFAB180E1498846800B2B9A1A29C184BAD25F0258A18147828EE8AE23C94A BA5F650785FC0ECF68DAA2E81CC27F3FE74848CAE90B2717F39C2F28240C9781 8BC66F3FD7AFC036F75BFC9FA4B7399D1C859508B76BC1EF9A2E702A0B7213DE 083052BA716549A9B22782443E222ADE62AB295A741C1448C9B907C59A00D584 3B9265BED050C30A5077EAC20A4565012AD267DED36DBEEE2D00F6886EFE3650 5680E902663D1D6328F602359B64CEBA6B75998C405340032BB48D69EE88E7EE 3D07563728E732B8B275E1E6802EE09A2F4D4C01141C4894FF403FD26CFF4F0B 776A8AD74871D379AEF3DE06D08237B4281A51EE9C480BCF95582F89025C49DD C8B32082D2D4A84CE99535703EED10A74844053A8AEC1A371D337B26E5F0421D 5AA8AFBD4384FFDE8A1D9C4CF6224E79648115E3DC9FBF23C597AD085A598AAE E24D4901E6E81236D45C1F0CCE5EA6BAD760148D864D18398EF32064941ACF35 E663078A618644AB719E08EE4384D8FB10CF66555D4C6DEE7E0EE5F10C2DB42C 091D2B5CFDFCCEAD4AAB2C4E1F21B028905EC8CF9A0C2F31264E1724F0661ADB 017FF063F6B125D76CB2458359BA41AA43B0CBF7EAE1A02814C2AA002A56A8CF 0A31EEE76B254895581AA4E71A1EE35118D8918794414478C04ADB4871CB2B79 69B69820A411C2D1101FE5D87D9C9DED41344AF6FA6BD7B9959C72916773D022 CBDCAB302453181DA09CFB200275FDAF3DBE808AE3836C58211F81F4DDB54DFE 4481ABEDD7296A92016A251760EE646E0C99F2203427D8A420C58370162DA3C3 F4BC80B5CD96134DEC8CC67F053823768C45FF497D0EB77488D3867058688737 0B434699E21239D91302F819D5B5C18D71424769AD1B4FBE3378C47CF19E2AB1 D367EFF0631FA75F87E7439155F91C7F103F3526C6E6EC72E830758E5000C7E2 F471CD3623422DE68CFB333088A40FD50F62C89796D88B1D5E7F8AD06EEE46C1 D0136DE87572B4DD3FAC664079AB09A4609F5F68F1AFBB7998253A46C45C8442 212011A30840D3336CF3F0C8C0A85E097854CB4743762BCBA11AC70D906E2B82 005335A46EC1F78D97BFB0467021444C89B4EA8DD83AD81E9BECE691EEC503A7 C7AA284C3DE089E5D16BAC98816AD7B16469EFDE55395FE5A190BB00DD4BE0E1 D829ACD58B171C17C4BBFAC658910A89526E926FC3A8268283E8082BA06763EC 249B63008595862345EAFBDE4D241EDB4FDE8C8963B5BF0F6AB5710C1D8FA51E 7A90D75860301A307CE266773204D3735640B846A1AD01111478AAFAFC54C8A2 223ACF46E3F0F9D3616E9918B34119B2CB8F13119E382E024B40DD3B400CE79E 4231857BB009A51312AAE651B7E8B784C4298B408800B0A6DEBDBE07AE7943BC 2CDED4A5572EB952E91B0863C50D7E72079BFB7638651BDB2693E3EA8BA57B8F 7FC2F79D15306923C5C64B2966BCE84D9AD722D09CE98ACCBA7EF01D79873753 B428F212373D3A63A5B93399EA12C7FF97A375E7DFD5D0EDD8151AA4688B6C30 EF750EC681430C9FC0C2E8859F40C25DD4B0F15281525ABB817B59C145EE05F9 B06CEE085B6C584946981638097E5F5292A6FBA8CB38E1D3115BBABEDABC2C2E 355708641A23FD2749166E522E4C6737F5C39F6189B8F39675917E447E68A7F9 B3994980444271F318821ADAACBF0F55355BAC067E64808FBF942338998F8D95 14D6BD7DBDDF52D7D14A9697997BACB5A9C2E3A885F2B71B4DD30E63EF47F2DA 4A1C8CA69D0C6FCD628D40055CEE90FD015A0F65D3C271A1BAE628C89A0CC1A2 CBE900D1537CC0C192FC5E8009FAA687BEDF469226A5BFA194024C7D4E1B0530 C78C2707122A2159724BA17BFEB49E35860503D95430DFF9E629D161F37D1B58 AC1DF92C2827AE781445D4039B702F91388E1183F08ABDFEB4E663AF392CB984 780AD164CBC1F304CFC9DB32435949EBC67623E3E93AAD8C034A99C9DB30A095 19B14C5A1F54A1B9A7D5AE243D08731F547488527D24BABA089E6459E7248D50 89F5FFDFCD94AD6EB88F622F478421995985B311DD16148AAF3FEAA717A94EB3 4F9A9712F77B72599E7A7FBDA4861D226DB96F7F7C7667364C698B3FD96D6BFB 486CD838E52EE8B47F9F172E34A4EA35434B64F7FB0A0C7C5A8248726E5DA24F 6B82ACEAB185FFCACE3C23905C1C7F42586123734F1644690F780FBBEDB82F34 DE9EAA414A9996FAC17E897DD4BE9C622B4E9E589BDD6375F60431B292116CE6 423404D541DE39B5E26D044A39E138A336D18484DEC0BBFC053CA3626BC4DA04 F1258D6ECCB572588DF9A3C3B1E865A105384D9502F85D027D1F02B72A1637C2 06773D0A16A86CA2C89C56C8AF51F0F463EF68E71A70AF72F0D76E193EBAB3A6 80959E4FB90776269FDDE9ED3225C3F844B3935959458A03BC0AAB7C63F69858 D678DE447A2E785BFF7B847FDDA13E18418F63F048197A9908341A38D7BAEEF1 1270D7B8C8A3913088B667D584B8F3FDD65E115A313BD2A7A83B6D48683A856B A8C9C296DE59C3F86777C6FFA3B43618B6FC3D5BE9582CC9858199B8EF1C0DEE 4C0863201B9C1967BCBCF530C03DC5F80D458029C0D475272C06B7C47737AA73 B166C41BDF1696726834077B0AF8CCF575F4A9164255CAC3A9FE3A2C3E74AF4E B36B91A9499B7C5BF45B7474FF213E073E33A6D785BA4787BAD9FCCDC7D35C7A 57642BD8027FF2BD30E5F50151DD7AD5E716275AC24E3B8A321DDB9542A0336E D68C983CFB23640DB3FB569DEE993E81584447F03DDDC9C13A8DCA2BDB86BBBA 4889 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /ffi put dup 45 /hyphen put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueID 5000827 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB3DF7BFF10C9BDA4EFE5F68A8CB1526990D1357AE6D2F7C2D2EF8496 4E47B39E6712EB8908A3265E5FAB40567E866C244814449F1E993AAB422C3F1D DFA8C7118584F2E5197FD4BFA3A8AE9E953C6CD4672C0FF51E41C3A919749C1A F06650DF4C5E17492164BDBCDF22609A74BFA7F69960A64B9F949FFC2A807458 8579366C4F41BDE1FDFBCC4845FA19BBB6963D65EE8532549274BAEBDFF24FA6 03235D1BE37C06B1938AF369DA75BF38DDBC87A1FF445EAA16E1895ABE9506B9 211955753E447865D33CEF007391D2666A046277A30A49804FFCED3FEA5EB2C3 E52EE14A9F75241EA10C91974CDA6236EB840FD44D6DDE4D9B3266C3B99BD38B D835BCA8CB819C073480FB972CC028D218F6A1D344CE1B63F4FBF2C826F412E1 6E0B05A26125865A14FD7B7030B478BB8BC6BC395335C3BA940E1C348267F4F9 0AF97BBEE253511940F1048E175D3569F7D05A28851B6F50765FEB6C9654FEDC 1BF52F535DB5BB90C1BD5D2EBF75E0AEBE82B20507F3C28A03746781018D4EB2 298E4F2C27ACF73FA73EBE43F014BB575AAD516C0407B29E1653375135ECB74D C91372F06FA8EF37C31AF3FA48AE65318EAA6C34830A5377ABB2DFA5DA53A574 433484BA1466709A4B186761655C8E482833B697673E847C691079E7F1DCB8D6 1AD91101D757B83E2090337D525AEECB028FB3C9F6A6E6AD2F322CFDC5A833E6 1CE4EDBF41FD34FD61630581D222F854A76C2EA9FD72796A7C9CC1F6C2FCCD16 E95CA05826A4ECFADA6A5FB83C41A7131E52BA6585DD6DD78515D8F7327DFC6F 9404F89280403F912C76EADE305E7A821D25D9A597066C3F25B8FC06930363D0 CECAB082D08D4C99D24B0F23DC680C9C0353397EB2A5D41BA32EC31BF5AA48A5 B700DF41BA4A7E5AE7BD55B7C540F02B99A31D6545FC9DA4BBB01F812222F4B2 E98C9C8E965DC2139C546412627BFD5A977E3702577C325323ECC08E61A0C5EF 685F6470820ABCAC3484BC36279C15613CEC013AA1207CC09F1FC192F7899DD1 6AF9E79558F421FAFC069792DC6CB0F25822FE326E3DB31F0C3C51A8A4959963 7BB306CDC781F10D4DAB92C504EA56729B9464C0304102AB76F7B8BF71924A64 9227674240D2A5818A3E2B7842066EDD798F0C70160564A8E05DDAD5900BFD0E 3B2B4E4FE8F6487A625FDC98579D74537C6E56B8177653B86673A6B28C8D32C7 31D9EC513D195E2C8A7CC6041936EB5274E289BDB2D245862AD89A5076B7EA28 10FA81A5566D2401E26A7DA2AF3E32FD0053E915AB215FF7D82D34FAD05B4342 0865444BF3A394BEAC73BBEACD9AC794A78F272D0864B25E76F532ED4B769E05 A0DAF9AA45F4031B3F92F215F90AD5DBA8D590EBFF958E9F71BF3FBFCACEC3DF 93021696B084F46F3D8E5E0FA2E2EE2B85DAEF69D54D8189F179568A5985769F 675C091C4638AA0C6CE29135AEF75137647BBFE1C46172A9EF5E4CC64B61075F 065A8AA4A0A867AC31FB55B62652DB7389F8DA7260C31370D240BE8042BDEC5B 95901A77A199E015F6E5D76C0D7A4208A559DD7C91FC633DF89D3EC22F7E1DE9 B28A0AD303EDC953310216E9015EE482CFB0BFCEA83F92B106AE749CA8119546 D4BDC5EB2099B5AF4D74225C4EB98D5517D3A642A801A64164AC57C26D8A0781 7BF8C4E60F0DF5C57AB5911297740FE03055BDED6E4B82FCB0125F5A8DEF675C DD5D8E14167B0A21CDE4AFB6FBB8411825241C4AFCE5219CC6304B1C98B0A7CE 5879135E7F0970797A81F83C5CA6101BCC2D573C8467358C67F26DC5372BA088 088FAF59375E3565187F167D5D503D75D9D7E84718FB7F61F21CBF40FE327D63 DF3022B0EEBD79A4FD05813DF56A61BCF1C125015E164559A91AF53E9D155CF1 05E71C59E846CE554EF6028B16AB1387B022478477860779885EED3EFBF95F18 0B63F5036294ACF83AA8BE0FAA6B8612FE84FFCB9FAA3736006CD97D1140B4A7 E815621C485F993B2AB474CF274ABE141EA75DC53DE7CA331A02A7AE4D91DFD4 E1586FE8B2257B9B778874DF82D15C692A6FD9D5D8C3ED8CCFF8C18B9A174709 1333C2D079184E180C9F3F8C01FE83DEE0A535DDD50172726F6A25C98D1C0195 9D5523917BC05BF7B5F56ECAA4D19AC4122365BEE8A349162FBBEE71F597DDBE 34488498DF37698636E361E63FE04793DAFB5B931240501F700EC5337658A827 5D16D193C5AD130870BD140A9AF7FCBFD11E5EDE4C0CAF219162212C5286B500 51F497FFB735B8F87F0923B6A6591CD45B6A2D354C46BF65FC5F829666E97603 0E426D7B050BA47F068E4CE1062912AA8F93EE59F90AEBDC2312482D5EA84BDC 3285A65811DE2F343AED8940E1E5C133548662B03C8D2F0B33AD158AE16DB404 8C0E5F7D1A4741103ADBE9FB827552B49B4FCA341B74A4DC58C893C1C632FB89 F8546E9FF5D399E05042269B70452B07D87B66B4EC6FB0B7E845EDB399202C61 F069DFBBC53F34F234812ABDDE9BE26A34C45636E47BD400CD4584A97C70EF85 7D072CEE78A1B8ACE75B375A2D9C8A4EDAD450E4EA9A6FE8C7C6662B4E9E37BA 2C9B68F6C169904A16B9D62178A9FFD28802BC607BB92022902605EBF12A9693 07326CB0AF0A868AC2E0E97BE39B2E49E1C5BD7481D7C4653A9EF0CF109FB3B9 42F8C4BE665C6BA6A56BEA50C9EBD7D11EC0C5E32862506E86B5849C42C89F57 53D4CC4F0211F9EF63894AFF8743A115E82F4EE3076CD14D33E2D75FF26FA223 6ECC652978F008D98F6BDFEEC9CE47205C89B4E4604E3F800D9235FCFB6B258D DD8B4CAC4C60402DC446ED03185CAE11BEB8E4FBDF4BC7237871D784143C6323 9084202E7E9038791C381A1ACF2480FDAB95423C0B7EA25DE2D37780EFC907F0 DB2035776F56B0CDBB3F3E79F05F75A1CF6FE032460C8CF1BAE16EE3C31A64C8 38F7EBB19ADC436588A8E14C0DBC375AC5618237339118C0B1DEEC12EC9421E8 A7BC9B4A36FB55ED7DE75465E12E5D1FD7496781EC9BC2F53DBBF14CD80B672D 9C1A9F322A40C5C6A75A8DEDA366AEE35E828C53CBB1DDFC9C77A753A4A25996 C4F289C3D53E6B9BDC7C4A1E9FC9DAC50B40B3B362CF0BFBBEE11184E0128696 0DBB88C5BCAB0825615490CBD4BB35E71D03A5F52AE68698934FD88E57B83121 85F4E8D0718735379792577AEF4D153269A03C4A13E2A3A47A05335CAA9CCF80 7C64EA4259BF1D0A49B5393AB77F00280E005C3C292EFFE3FC6C77F4D154E166 59AFF645AFF46FD993096CBDC0A676233451B0F4169B2FE0A242BE52A23DD2EF 4A4A7B6DD75B3DFBD65C860F34E2114119B1DE8AD6A07B3EAA0DF0990569B4BA F218492C61E25AAACE415513903EF2893D4D942B6D9332534635C71CE946C641 93E92E696916A77DE37D34AD4C31DA6F2956A14437067BA566110EEC2E5ACE16 6037BB1362FD00365B30B28E519890481B84BEDF604DAB0930A536F8469595EC F0C9107D76A230C39CA2572CF159791382A932D7FD7AA8C4CC79E72F29638D8C 799004B0723A6AFA9D9ACE61723ACE1E95AC2CE4D922625DC6E1BD8A6B2878A0 427BE09895CA7BFF1893C3B48E1DC307A3F5907B22D6A94ABDB87D3C7F16B142 6150625716FD1824F03ADB3D5C21D0769FD017FE0D1FDE8BAC96F338B158A4E1 6A869F0FF50F25BC9034396D2DCB75BA79A64E6A75EA034A4210BCF3E16CD9B5 52F830F3B3F5ADD6AB6E9099B55D6D19840DCBCA2F3C87316F3ED49057041B07 FD8FD04883C15F71FD89C5887E3BDC7F61C6E10000C6DFEA32A2D52BBCCEAF97 20AF047DBD84615669AFC5A873FDC6BDB228FD996E5811DEFBCB8AE48A6783FA 27DC7643FCFA8F9BE77F129BAEDCBE883C1481665060D70C08CA108821C149CA 4D5631B472EB1E68BEFD5BD92E476B6C331EDEEAE4424311964FED501DC7D64D 14BD29C366C3CB12D64490F04FFC70DA6CBE64D243698DB4E3181CFB43AFBC00 6D00871CC8A38E0B7E754FE4E0800C04EB54F5547D0188F68334DEEB23FDB282 35A3CD5EF264110630C903B0F0D83739DFA2ED1A1D1A2B594A3285F5BE94F616 045AAFABD95890F4800A8754456260EC2C807F61463AD8E51F7F959A47DD5BBA B94675C8CF2C6F1984458ACE959BE6DF22563A634B1B2C31716F97E88F7E3364 B92CC7733C0E6F0CF5FE54C578670D1623C7CEB5FF663E0D89B3CE54BCAD2DEC EE26757989F0AFA69B4450A4C5B4D211AADC75F74A872701F5C7804FA6A8D17E 7196E5ACE144F37DA575C16A9F3E910697EF27B48D389B604005273E088D5114 2B98AFB9F146E9B6A23DA5EC56DB005B6201E71B7A2818C7B24EFDE9334E2F40 C5940E81EE9D985E798B2719D9DC229277E887C7E98C905C44008705444E8E6E 4F7332CC39AF61E4CA4580EA11FEE68B2B747B482F7C1EC5023508503C134901 9B8E160DD36F7F4584129E3EE3594BC92D6C406BFB556F8D72F8CEF140008F79 1559245893D51FA07E1054B2574970CA93A236E38053A355E57B645A045DB20C 9053620C512802B8A2A82EF2116513F27A421D20C56FDFD2E7FFEC3323AE9FCC 6B70D841C2F85E23CB645F7E4C21DDD9DF834FE727BF12524A531465A0C735D5 13A2DB69B776EBB3F9F7732F1D18246A1EE0CDA71036429E318BAD4FA709B6B1 D37ED06844D4177A97C59BE75DC17D9208749B3230F0A57263E62605173F861E AE9131468AA5C4057BD801893079888B9FDAC3E24AEED2E27AF37726E67707E6 A14F44DAEECC426110F15E72218725A087013F687643C1E52CF2C5EB227958DE E8397106F348520CE6E3E20D2445EA07EC4B164861869E51949880D373671204 FD475B543E3048A9C7DD132C5574835BE64FF4EC9B801CD8ACE41D5FB59F7B3E C570FC001DA45C60738B91827E8A469FE844358510E3A7B36EF11CFCA1B46BF6 F81145E5D4C34FDC4C85388C5673F20A0BB51F01E35A09853DB29A624D692FFA 58A825EF71842AB7FA90744E53806AC1357FEEACD01D0FA5B4941B908208CDF8 B1CE46E498DA5D13608E27091F74CAE07D19A225D0FE75C1A44DC028B0F273AE 43088E8038476948A9C0FCAD34D8A7511E0D66BB87D4C1C95CD81620DFC0F56D D03B0F17F0BAA3014135EA487AB1BA558D211F7753E67757235120A54BCA1456 B850CCB42836BD79A7A94CA4B04967002061195E23BAA10CE9573F632CDCC739 AA510C374608CDD8E643A9EED4D077725E388611D146291F9F995DA8FB314544 8DD5BAC50C8268EBB41043B96948571F8203A28C24AC3DF0EE7053E9B9946870 F7CC389A921990FABE0B278DAD45A346BC6B7986AF63D780FA8D238CE0F32CC3 DDC371FF30966AC7943571027C9145FF1A71CC21E9DFD978569251677754028A 36576AD9370CD49E6D06A689EDA1A89CE926060465E9FBFD61174B6AEDB197B2 1F9F074EC7EB73BB85076402726CE56223032EE7C234248FBB5021CDCCE3FC3C 973BF0CF65E5F87CDB8C906D05FF4FA7649345A49E80B4CDAB73326422D58A83 3BEA208D565ED27E1422AAC01A140B5EF2C3DEAD2B2D0E2126D734C888915B89 E5DD6E801E9EE5BF1BD693F963A7F88635B55E7485441D377FFA0323F93BA09E 7C0CB3A67F7FC248B200A2DCECA144BC2E25764091E2393DE481482265A8750C 8E8D48DB00B6A3E1E09BF1F664E57D14630229A3B7DF0F9EAEC1DB7017CA3D95 6A1D3BAC7DB3AAD1087637864A8B12723BE046BBBE4E6A3610150EEECDC7FD4A A822CBB636669EE7D79E3523C7A8ADE886677D2D17E7B25110B8A29D29D8EC04 25579EC754AA5F75120C87D21DA8C95ED66156F62E7470C3583179A431338482 1BD7F01E98BD892E043EEA47C9585B6CFDACD19862D2CAA47E2A372AC93775A7 C9C6EBF5A270F31401C5B25E1CBBF3B374C53830D7278CF46F7D1BB5E2FB9AB2 57856DD85C425166C83ED0E5FA881BAA2039051FC7B39E4DFC3BEC5A51588777 B7CAAC73272E179B59C7D81CBFBAC96690313162D91407FE13ED90B9B53252F4 D18C059A80BA093785A05C672EFEF9815050704A59360FEC9807B113C67DAA6A 537E66305FF6EDA8F78F0AC04002B94B12EADD7CB3E982020AC05165193861DF 58B5C1F2EB10386FEA7A4BE27066B3A617004B2E87FFB6284CFFCC406E6CFF3A 1C94E42431CEC653E0E501442E3363AA2FEF93F762F1169470209EF8EE4BCEF2 2864071C243CB9283608E219AFC1A13314BB26483CBCD68C31274BB937A58694 24F93E99CBF4A987973D43B14DA1AA239D579FDAB4407E7838BC1029F67F7634 FE9AFEFEA3BF649F18D753ACE144D9710530DEC33F2377D676568E5408F5B119 A5254E7DD1EFE83A562E486B8B4B46D23EECE5E7FF032A15271B1B3BFB89CF11 59CA78D06B10015BE46BB82C1608594AB290944C1C8948B860436CF931C18D7E 972CC7B75C456575EA19AB48D559B3B8BE614427154987CFEC15D066AFA56561 56443953EA5E3554E67276A35C4A8F7D040164995210B97F58DB6B9B32D8A654 A7E9EEEF635D0D7B96DB107053D9E6C109236E80E7E36A15F33511693FAC268A 51B72983726C45D609AF53BA60583FE35C658334E6575795C5993F849328884E EE34AC8F5EB09B3A3155479DC505DE4F29960E2E52240892FE191852B39A5C94 89472F63A4A5416FA936FB5C0DDD1B7DDC9A631A9C35FE202765069FFCF7D01D 22A6080C1FFC75024D10B0F7D32BECC4F93302654EC55477008FAC3FACEC272C FEA62A2F7C0E1DBFF8C19D237991FAFB98E60B4BA93B8DFA4B15075E7CB4DF2B 369CEDB8FCEE490E4544FC3F4D37ABDC1B10611FE782769EE3E93D1A644FD8B5 05AE7EB9825E7CC4BD77B3574D7877161D15D1AA8B39902CAAAF43DC47FFB9D1 C02A9EF6871224A6DB61DDE16EF8E42DA0109C95E0851F36047FEF064519F497 3763F92DC55BF1010B86BAC4E2D42B0E7A8DB26691B818F4D78BE20106A4388B 78FCC9BE90C742ACEC11BFEE85798A84F5ABED32029D5176A36C59599D961CA7 AC8511397921F99B4341AA80896E629F88C79D53B6669D6CA70421EFE07D307A AD022AAA5AF5B31F028605DC694A455F29DEE863657F46B5B73563A3B628BB0B CCEB1B0F6C4BF31F27E76A99785B93F6D977529491889E8ABF1C4A5181E7D99B 0CA7B5FAC92D8715BC652210D1677BA253A4609E1DF1AA5C4D36C94B145497CD 406596F402B5 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 42 /notsubseteql put dup 63 /emptyset put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 8 /circleplus put dup 15 /bullet put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 29 /greatermuch put dup 33 /arrowright put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 50 /element put dup 54 /negationslash put dup 56 /universal put dup 57 /existential put dup 67 /C put dup 69 /E put dup 70 /F put dup 79 /O put dup 83 /S put dup 91 /union put dup 92 /intersection put dup 94 /logicaland put dup 95 /logicalor put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 0ABF1D42C5DDD0C384C7E22F8F8047BE1D4C1CC8E33368FB1AC82B4E96146730 DE3302B2E6B819CB6AE455B1AF3187FFE8071AA57EF8A6616B9CB7941D44EC7A 71A7BB3DF755178D7D2E4BB69859EFA4BBC30BD6BB1531133FD4D9438FF99F09 4ECC068A324D75B5F696B8688EEB2F17E5ED34CCD6D047A4E3806D000C199D7C 515DB70A8D4F6146FE068DC1E5DE8BC5703657B5E24D46D85517B86B4C3D5E80 B28F13C7DEFA38307CE8A6974E3B7F1031EF18CD93721EFDA110B5B7654B2F47 E3A73ACE038497A1D485EA5D476E88E931515FFF3757EC48EFDF55243DBA3C8E 56EFD21BEFE16C034EC6FC7F34822D362679DBDDA40DC302F2551D31B97AFF36 091F062649BC08EE4A3DE7CFC0BA0099EE8BBA26A0A6ED65F476A77D46C3331F 75A685C2CAA1E2CAF2770A2094E94D3B9BE9F20052B2A4034F657AE5F27F8A08 2E21C952B15ECAA930ABF14060A2A3421F4B86E154474A23E79FA496F7725C9B 7FFB9D389E78BE40A4DA2EA1977A193A896CD07636E6BB936CA8A1832FCB7300 EF1B0BAE7624A3AAD4E4386F843261175669EE8158B71E9966C51B4CCE5F755E 8AF581D04BD7433EBB100B0D51C274C2DCEB2E28C8DA6439700934597E319EB7 A12B4555CDBCBAB493FCC846CE45FEA13B7D15CE3348C57701C71F933D741819 C70C2ED71FF1792A17D4AF1D574F3A9FBE4B79049787DEA99399AC7DB7BB7356 99E4BFD6F896E9963660D24034030DB13111A64190F5F7CC8A471BA47191D6CA 9EA9275FC35B3D91A9B7E02D119ECAABB2D62B03C9FDD3A0FFCA4D2ED81999CD AA150FED3FC355456BB2D45DC3F9213B1D4F9A03998CC4B289603AE37BCB9C34 184FB4D1461D6FE3AC469F785334BB497FE3C242DF936E4AF4CC85D1619B77BC 4B07175542714AAD7CF81CDC6058F8C892966AB9AEC169A9D3865FFEFA3306C2 3B6A72AB9B74AA079364A31C52FB9FDF3D21AF61B45A3E6EC0DA95F381714520 334B753487E2FC3B164799D7CAE9CF7C46D7959FD6E81F1DDCD994245BCF1654 A5CB15859EE580D642E4ABC91E18941C0DBD7E4BE1CA1DDE2A99744E3BFEBFB2 B18D07B6D6A254AC2090662D3CE0A46BFFD9D5791BB333461FF604F30C683681 D46DB118D65F384424EAF0F4F8A95ECD15186384A571CC3ED8CF0F0B33BBDBB3 390D0F337058CF967834070EECB173D5A6D8A08A3B918D5872785C7038822336 8F1AC41E4A95547FF8A55E96B71EEF34E58BF6A236F62E7497824F7B82BC3ACA 8A02443B87F9A39C9E050BEB840C9F90E07A86F00C68B0CD35E79E1038AAA2F4 E0D08B80D6CF4E8814EB59AFC36D2FD23232B37F1A7884096B4C5F8DB2276D2A 8DD65C6420AF17E76FF8902D12AABDB13FF35EB9BD55FE34A118A59D58AB0E32 682B98E330B6E059973DFA40DC84C45737947D561BBAFE10AC9F9835B0A006E2 ABF8CB20395EB75B54A19003723580D7AEB5227EF03B9BB045F61B9A35832291 354306B3BF8F4334E79B1DC3290274D50BC43034AC7941DCF51D7A5772903FF7 420914A0C77D71BB343E928BEEE9D512502B55A8807C8249EF3BC3FA04785BB8 47A5DAD13708AC6C4781253AE439D2848879AB9CC634FF85FABC73977213ECC3 6B5686D077B7D8C4C3A7167214E0FE3B59DCCDF96E76448D2C0B4CF8B8693A0E F5CD996570168A1F0CEDB134FCFAF11807AB6EAE23C3270E483DE90F00DED8F2 BF01C4E3860CD1312BCF4F2CCE0696C60537B0D345AAC02EB8A5993BB77BE142 626585EDDE847BE75B189EF68CF4402B177B81E74DE968B1856FC72AC743323C CA6DBE49828582A47D3D9C309E9B5C5676C5747A0D8F592C7C01FA6256090275 B9F32465800FE03DFE447CEA194C27A6D85F47E96344E9C6795EB2BD8EC5ACE3 C9B70F6CF4E115A4F0712C371E09102ACA15155C7373657AB5A720E02C2B2C3F 7896D7B2F08A03C859A54FDD0357A63C09A4F53986B9C8771DB1EB6E520E2C8E 07C2D9CC7BB821F21E4F7756B0AA1D6BB409EC600D9508B47BC89CF4FDEB85E9 C48F44A62EA03E3778E73F031B4F3D5261FEF2E33154563BCD6B671C1E223C85 52144F5FB84EF4A4383CA56D9156ACB95EC23DC7E96ECB4DE57DE84361437ED4 47AED5F937B6EF8CAEB83D9C2A159604DA1392CF9E5EF3C3A013549DE7DC8D33 C72DD7F81CDAD8D1065AB92F7515597E3D754C0C9696722B9E48B808CC1F4AF1 4921E0D3FAB0EF24234676F0587C435C49DCC50B36B414304977AC3F9E579D18 9F04C769EB6D1356B7C1BDDB310B7594C1F7B8094E8EB23422C6278A33091AE4 4AF10D0E20DB47882DF91C59C895E8BE7EEDF34FA627F1E9ADAC8DA002D2CB48 3CBA2868EE81455622053DE7F2C3CFCCF38AC2BEBC00F282096EDFD9EB55FC44 A2FBBCA0616773B95BA587C5523479C82E3A169BC825566ABFB486A7C41E89F2 24ECFB3FFC264873609A8D8A9195FC15C9C2FA9FFA21861730DBECEA4849091A D34B896F54E5CFCCBB4BF37234F066B49343B33A043BA0480A76B04C4B136299 0BD80482881D4A85D25971D2E98718C726F481FDF1224C8547C4B586713ECE0B 2F178844ADA9E16393C4BDDB4F9A381BBC9361CF73199DAA04C7967750DC31DC 514640D65EFD870FF7373BAA305EC0064E6846E91E73F69F8F6145482BF43C53 14AC70AEBA55AE553867C0B44251E404EF5B81451C5BE459D6BE931FC811EB9D BF066B439BB14E558628942AF699EB0D1300411D9CDBDBD332617A7AAE66F7B5 0FF1F89130CC33BF97FBE32E8FEE6D4DD3D4DC6E383C25DB7CA696849F691493 660428731363D68C0C5ED4B6EF1228EE21BC2CCF8617C9FBB30883A9B5D1489A C20C836C918F3AC9611CAFD2147A71351DDF669E71A007DDB72FA7722D65E4D6 F74BD21D263611F1B0F6783A3446BBABDC29CAA5C9CFD8CE2B72EEAD66A14DD2 BB3904BCC2787C650072745DAFC723EAB6228846EA9FB49A51F018B5D90F6E2A 44E3A2D9FFA2DFEDCA3A9F405FFF5756CC933F29E20B6B6B239CF9A0EF2D8F87 070D674EC6D7EB270DB08ABA88F0A5AAF1D0EED4A0680655E0E6397659B8889C 13E54732CE8CA161445900660F3CD953C058534DB89CB1C75377351A5FBE1194 FA92E2B3EB88BEE53EA9ED63991A493EB7D0F6B109AA7387767A9F48F9ED4304 89875D21EC9DEE2E6161AEF329A084A3EACFE6E2100AD64DCADB5437779CE690 ECA251D8E3FDBD5DF76E4910AAAFBA686CED63BF1C2BAB247935957915E02DE4 4B8858CEBA20583195E0A2E1F6757BB797B0E4C3DB0B12A9F308BBF13F01D396 D8D17A625B9DE321EB992C95005019638C99006FE156101EC590862110FC54D0 56F04142306FEFC9255A44DE051BF69F33EC2C23961C51DB72DFEA00AF751BBC 0D7DE9D894A14EA2C6E00846582A8E48FBA90CF9A12A6E9FA868F7D7A68EEF56 669C061858501EC6DF81398810C8A4B0A8EFA9FA402627800A4FA34F786F6E3A 0B0E65FB6A082DE09CBDE85D69A17F5C62C2204716841197A3361EE6F5A91B62 D37A890265631F5D9D44AA185E7CA519837C4E5141D07D183C9760660DD6790A 13C63F36C1A58103A7C116C7C3E3C2958792A8F56671A4C3937DFE875C267FCD 075AEA29129414FF1A29BF2ED2E15E3C60B6FD738E4FEDD4DA458CD54B1F70D9 2EB9A89D708F217D9C2C99A646D3C4B0C33EE278897673A1835A1DF3A79A61A5 74A670574E8E2843E69955A5ABB8E8564638544FE1D79310FBA0BCEE92C4CA72 BDA86A816F2A55BF06DC1411952FB0107D1720CDC32FEA36CD6A871166325293 3E7589356D286D4712B995634F553350182691F0708BBDAB3136BA0A86886D70 A23EE12979AF2F3E92044E6FE2B4662B4E018B6B1417F34A24A1186FD63B9D70 B431D134B44AF9ACC580620053254F6900D283F95F633CB0CDB782D1AC5770D9 6EDA3D90CCB7D50B88242B574AB81DAFD2FD77D50336395FF7E1C92C21CB7060 7A32E085532B8DB465EB29353B7821FE71EE72CE0C8C491212C26632FF907A92 7899D1F50B120BE99C3099AB5FFB6F9F365644F95BA5102F7AD2A56C14EE2B58 6B0699E0587DD8F8E3584F10405CE36F5CC26030683BCDE1CD1AFF8C2CBA6D97 EC00166E434245E5E5879987D44CE52BF44AC9FF6204EC6DBE4F15A4B76EACA7 697E80D5129B96ED622467F8F2D51FAEC16A9A8B1315FF98187BB53C9BD430BC 1A0CE7978B016ECEAF606C7BC02DDAB751FF3F8DDA3ACD4EA8D7DF83409A7157 9853BD6E254384CEEB6DAD1CC22EAD78C992DC1376924CB5187A714256CC6912 DE80A683A611D270F1689D8DBD64A1FCB31E1A075A3567376D8BFE666490A63F 8E8B059238B52EE559925956C907C763373D2D61BAB399779DA1D1208EB215D5 2BA19952BB63BF11F56DAAAAA7C0BEAA82F68448DEE719EBC2553C023B578FED A27102DAEAF13E31F676520AC51857B53B4E57F4E02E5DEF20F96611A0D2E1F7 91A33AC4FF9109BDB183E43F57F12CBAE389F8A87EFCA1309C77ED862BEE4746 2D5AFBBE0EA34CC4186422B285D25A81E579B661BA0F5B5C145B73F5E5BF2BB8 B48A02F267AD67A853D12950A1997E616759776B83FF754BF545CBF81C9942BE 985D201F4E47A5AED1EDB8301167AC4861F740ADBF2E008A2905326FF793A795 C15AD537BC87001BF5A890B48077379E8F5258630D2A2AE1DB1FFDC2EB73BF8C 9ECF33123C7C1ACEFFC530B60D7D21E8DF4BA4218A57A2FC63C39304F10DAE15 60797568C13D23EAAC820DD84B774C843468B6D69FFB33E01DE3160631645ABA 06A6EB5F9BFF71B5DCEC363A2747C4612D49A18BD95D37B48D7B619A1FE95014 81BAE3645946DAB14E6A7967F790E68D0814E4D1AFFE73BF69635A764AE82F61 69993410C0B8DA179542D2CB4345EDDB3ED7A82F65303CE80FD1A57898EFC342 0DD26A1209974E0A24FB58ACBDCDAE71E062111538C92F000F4C89DD5BE0DA97 30090EF8E0496A9FB7A34DDC9EA34B9C71E4DD218126950B33D2728F59A632A6 AFACCC7F65746C98084D43C53DFF27F2111FB876F9813D1F4A484F3D2C8937A6 28D9935476058AA02F12BCFEBADB4D00D2A48ADF64C61DCCA680F3C9D9D8BE24 BA8E90D8DBCE67D87BE4781DB02C164163AB9AAAF3D3DCB373DED80501F86BA1 CC0E05F3EC1AEAE2B12759BD57654391383991CEB64EED03A2FD5822396F67CC CDB35E4B5E4506FA46D5531D8B11D9D217EC95228735B6DD77631D7F963A15AC 4FBCA53B46B561A52F5AE46AA87C407D1D97E1A0679955CFE845FEBD4AC40B75 98A2CD9A51519A26EB58C8DB1850C9C94A9EC7B1C30B40DCFD1D4EC66632A32F 2739F67E4A384CAB9AE9A8D3BE0A267CF0D282A1FB273F05106067EA50887A3F D0DD616620A00E156D8A5A8D9665037077477C0665416648D3A3A4B61617E637 8AF0F00BF2371B61A83AC1F8508E5CBC98CB79942BAD66813F17116AFAF91451 D2ABD08E4107A023F8B86F18AAA97DD11F366DA38D4953007626E9FCA8350B83 895278B27C2E5C3C99341E7A58DE43A776660EA09F82848F5C179889603EA149 3E25517127C7F0AB097658CE0D379E127CF530449E4A63271FC09C8B15920E92 8DB794EC04F5CF5A58959D1BE4D8AB6ADA40C617812EC917BBD93093399AA8B5 86A2E438564240CB2BAC5500AC07B24AA1D6B12AEA3CD2C1C3E2A3A015692A52 8FA017603CA322338E5DA4C235CE65D45A1D0F24D9ACE8A4ACE47437E249565F 211817F4807EE7F70B3A685672E5957746E765DF21E7C78775702FC14D742213 E4F1AC4CBA550BF9797C66123A1F5BFFF737080A5FA0C4077B755E40E74222BB 1D7C6357ED54D8513705C1B557B432BACFDA60D5C9C58E48E4361515848DC916 1117E3B78C7B2D4EBEED4B7203BE69292EF54F391EFD48A4FD470A5757118EE7 963ABE90E4E3D1D89E70CDE0434A4A246352BFAFA974CAF8EE4B835FE2741D18 FD2730A29419CEB2A0F725BB9A9641C2BFFBFF8C08B845212E398B4489FECEFC E097714AD864CA0FFA57721637FD3076FE74E579CCE3D321EA248FA22DD81491 5B020680314FD2132B9AE3F3481E4AD5FE60BB62D11F24381EE326D40E7FD520 416D54EBF6F5656010E610FF56FB01D7792D8551E65EF5463C60E674044AE9FB 25A085530B2F9C9675459A179255CA4729DE5FE8D6F52A687F5C3EEF90F854D5 1C62C28F76091427BE310DB521DA21D10D9D97E83F454FEE65163EBF6E3DA80A C12B86987D7928E65A6B41FC1253AA9190EA1DFC3DFBD06F66A456461A41A4F2 D8328202D1378A771A357AAE54E4AB6A4CD622FE8E017B97561ADC2B2B69D5D5 AB03DFA825404066FEC91DF9BDCA30CFAD32A30E3139717264B63313CECB0E51 D103BC339273EF719DAB7B11A4FC8F469DA94110F548D670390D58ABEC62A411 1685786CC1B2520A566E3B9BF85FBDFAD684ADF387329B13141D4EE65899E572 9D5DFAAABE3DE52D4A3D9967F301E63A678EB4B2F3C751E0B39A22E8FE56F4A3 6DE0A1B82C9074E6E171C968E786CDC31F18DF99180509BF78D987D7891F32F7 2A545956F8021B274082DF4EE0ED639B485E6E76AAF68D496D2E58AB56010258 D9B78D2C12EDEB8F7DB30C5578D997FF0CE22BA652D3E95947E8815034C6F3D0 4CAFBA8BEEC926C8B2C7627E52D5F530EF18D645D0470CF65D52D3A7EE14E16A 10A04F2E83BADEB30E3F63EA2E74FAAB179C8C5BD1ABC0B280690CA606B5FF32 DC0EBEC33EC7A5611CCD3E201D99B8771B24A632DFF19207DE49F5F9060ABF31 6197A68DF95A51816116B818E8C846 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 34 /epsilon put dup 70 /F put dup 72 /H put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 83 /S put dup 99 /c put dup 104 /h put dup 105 /i put dup 107 /k put dup 110 /n put dup 116 /t put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 22 /mu put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 69 /E put dup 70 /F put dup 72 /H put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 83 /S put dup 85 /U put dup 88 /X put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E 6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF 8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE 03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 AFC0E2F840512D321166547B306C592B8A01E1FA2564B9A26DAC14256414E4C8 42616728D918C74D13C349F4186EC7B9708B86467425A6FDB3A396562F7EE4D8 40B43621744CF8A23A6E532649B66C2A0002DD04F8F39618E4F572819DD34837 B5A08E643FDCA1505AF6A1FA3DDFD1FA758013CAED8ACDDBBB334D664DFF5B53 9560176670867FE91BA0A257699E5EB87A24163F589F479E40A86E3ECA13D1BE 399B8750D2EECB1C08744E0F4EE6BC130A22E063E4F0CDFE3591E2F13CB637FF 4866211A0C7F80B3123D6DE84ED16EE5CA748853355E8E7B46689D491F6D3681 119E1C224901A2C4595F6B0F3E3A2E35659FFCF6C51C44CFBCA2F44CB3614F51 B146E967B1A6DB6C80A83A7AC4FAFAB61D897055E4DD14D8DEA78B6F89F607D6 576D0E4EF488E4A8BED9FB2935DE615365C4BE2E7D1CC7BEBC5FF690F78C4578 65B19F2D1C99160B984174F17C722691206E3BDCBB2AE910C9015A6E87C4DAB0 69CAE6BC31C4365EA649B15A46D16CDB7EC87C1FA556AA7207F7306BAC9642DC 653D563001D9959927598464ED48DEE53C5FBCF36616E374BA22182F322A8E07 980CD0353FB51E95121677878E59328A7FC8F190F6B0DDD83BCB2215978B8BFE B36E5378E8A19C54EC21168CED8839320C3D73A247A5C437A3F23733C10B44CF F6E31A90B6F5C51B304B7D3AF1E7CB1192F2AAE2E41A2A7816B751F77F9C9FC3 5378C8499FCA37809D86B9FE6BB4EB3B2D557DE9DC2AD4A2ECCEEB9B52CD2841 AF3CDAEE96490FBDDEAD3832C063B93CA4DF30B82D540E6AA53BE348613D79AC 99853A58059BE9A7B09E6C8562DABD5D8E4A618AE9ED9451E662CD7173E601AD C8D69E3D561026DCD32A3F19734BCA8F03D953C62ACF6CA6BB08B90A9A124139 C2485F3F616303047991E56C43DEFAE6E6FF0EA5F2C30C4BEA67A944829B20FD 6B3A0214EE1AF8A5AB78761017B01F60E02C75E45667099878935490A1008C08 959FED8831C9A4A5DAB25EEC90923744E06EC01F4F44A4F026549216AFCCAA98 9A6CBFBA9FB92BB926A5A5F645DE5E7BB959DF501D61350233372459BB18E21E E45135B5131307FE4BC243A04403DD4C1A1DF9A4B5431C5B9B8CD9ECCCB337D5 4531A7FE7FBA8C10A34F67D882B7386C68E68CCAC271A129663C2C7E37B3E361 4C0F7823C3F389370C703A39D1931A5B9321724BDA9CB107C6B5C2DBDDDCC83D 4E825D5EC755875701CFDE6A43BB8F4F5E5890C26AD6E9D31A92D49D6B544EDD 8A838238456C83A04FA83482DC957C6E9BF4E3786B504FD93A3FCAAB0A7980B4 87341700B38C08482CC1B939B641B3DDB7681B1F6BCAEBFA08A4394EB2F4FFE1 272029C1EC3AEBD361F31BB75E2B4760E91995F7EC30093C3E178020F6BC42D5 04E0A7121B731D879ED3955AF2EFFDE221ED6A7F027DDE4A313960F314336503 C61BB0E8EC1CC81BF08D66DE33A18B222178629A5D2A66B4DFF9A9459F649D7F 4A1C6E7660560BE3F72587943D9F8262482E82923E3BBF43905F552D79B74A50 A419661A93493D2D3CE53E1FFA42180B01811AAF24D6AF389BBC100BFE972E32 8693DC240B30504046BA26CC5C8500D3FD1AC57F27909C7EC1B435C3034BA593 28466A7B438483A547547359A0714FD78544F0854805484A1B311F989CE16751 201305524B50D680E6F556C05BD51C83EB5ABB00D93C61DDB32CD9A478802007 C8A54FAC4DD3D3E0A6E2A782AC01287CC3F288446C7317812BE5E75B28B0CD31 CF9B225C12B49524E988500B3513C3D4CB65FA7D1AED65ED90D1051B1121C4E8 7459D657333F0B25C5CE3A7C4C9253A79535CED10FEC380AC35BC660E6D22966 FAF54EAB7F9D8938FDC3454A09AD7E3EA822E8285E7C31F8EAB3C97454923C59 1369F6A8A95D9631DD126D901FB2E823357956F607C8B32C44B64ADD7EFBA88C A9E1CB3A4EDD086A0D7D71416F8FAC9C04DD308EFEF55747AC82A07F1024C65B FEB38EC37218F5A3C0AB84CFA866EAACE2C5D9630B6EF138E228CF45020F26CC A35EF89994DB8DE9DC623CF109D6486C5C26A23E3C8FFA9E47213A3BBEC501E8 4759BCBE300F3D664426011573062AB00C5D496DA817516BB87D1C2BEF53CDD5 02C4E23C3ACFBD1E9153CCAE2FB8D7D389EB423CC5D7E5C5A5C164B81FAF4053 937D9F997203B838372E7C511AFF43289054C4753EA6C15552D6F4EEAD51664E BDCE11F30B274E32AFC68AA3148AC7D0AE6175E63296E9EE06CAC87E0CCEF615 3EA54BB8E609F2F7141212EF992648BF4626D45682432F173BAC164AB6F519C5 D13165C0F660600B671DE76EDE488AE4B2D5D1CF97F5F114741C901E3C40357A 1BE6FBBD85E49D73443B8AB4AB1DDA126834187A62C216CE6ADEB5AF1EABEF36 DF3C187B786701A42D77B0760FEEBD3C764BBC761786C98F6EA454B75C1D87BF B6B3307343CED4DDB6348B1916973C9CAB412C87E48CCB3A175F2CD7D778607A 278DF7A17A3C9A16CE58D2EBDF1E908CC2CBE8B3400CFF2A2DBD7B930DADA5A0 45FC85B21B3C51A66E4247EF29A6DB57621BC7AC0DD1448DAFB3ADEC29387AFC 23378786A4EB9FADD27B87BD2842ACF2DB069E37A11DA39078DFE0F1B990752A 39B3DD5CD0AAAA659585AC0128711BD38E68B0C9CEDC9166F6A681FC5019A234 CD78C5ECFD9DB9FD0FBEEA0EF8DF09C0E9106148EA243A7BDB16A0F1D3B61778 B00724E529693F42D8D23F77E19A1EC2CC7E0A52777145361C6962039D216943 E0670EFCF48F3D0AF4964D81A08DB43F564E5DC5D01DF7AC62E43E7CB9349412 8A871AFDEE56D5DE037E591575B488885E488D3FB6684DFAD5B6DB9E872FB21E B910172BEBE6B99087E631D6698667A43578FDAC049488A8F1F94470971C0791 2D39A8D05AC682532E888D38C4305DABB1AD051B588AB89D3CBDAD29B1DCC630 F3A065A958C053B92BAEA4AFA9DDA7656EBADCA26756795267D801D94CAADE67 838171AD9BC14C8AE0FA36A0AC4B67ADE39CE7DD9F5A69719A0BEC45CC77B41D 92D040CBEDC3179EAFEB3FAEE236897CC6BCED3B44B090B5B5AB98932E7A0FE3 382EE3190A137C1B85782C832F025EA9D882A3D132A93A990BE630263671FF91 F6F0DCBDB6733F8BBB7AEB71DC39FE7F2FF6730981765C842D3B1ACF983D31EC A2F2616D447018C85DF3697BED0B1DD606EBD261D121689DBB28B9B09EC2D718 9759E70ECA65D9BCDC77C84DA7D661E441E6076A10EB9A1A6DACA4958D67D6C5 863EFC12289A67E3FD7D1FA455E6A0F7A25A8BF211959A301BF3EA9F495B34EE 9ABCFCCB8F8EA137B0A9ED4C39EE87AB0704A71E7EFB58F9193280EECA5D8F32 A868EA7146FC251918C655C971E080B88F7144AE42C2B7FA036BC1653068FBE5 B747449684E75720AE65956A94606FD9E39BFF8EAD349C46BB141253B1504511 71F20C28261076E6A0BE74576832E1BCA729674F4A39B7A96FF910A67FAD1997 F285DC809AF6CAA03A323FA4A0B9CF6E223C7943AF703E40608739D368771DBE 25EF3E7B355BE3C89757386D333D70245CD3453A30AB8C03A57287941D8DE5A7 6FE6A887FE336FA10E73ACE32B9C225AC70B94BFABCFEF0EAE22BE90DCBE5CA6 F2DDF61D7C2200670BA93B46D34B4B8A1E7D9791B481C9F629DBA70993198E4B A6C7D2CBCC43E967B348CF14EC6E92FF2A1B81226EDC0A5BE78AFA36993BDD64 B8BF2DA37FE4059B9CF87DDC3835D9380BA01DC431C8D08E53340017895C7575 1FB2612FE2D55C8AF524222A29F30F586904EE82DB845482BDC810F911A3FFD0 D4804C6C26B6D916006827F8C78598E55FC93203610117C256F05C35A70C2DEB C2C73CBBDB3508F4398418F3A93BCDBF2643066AAC0517DAAE8B302E5CB46060 7E410B66731751CAEA7F84B5D049F61D62AC842E5F975D632F3B5B4FD9DF0182 97B54EE274582768DE6AF8CF657CCFE6DD3114741B6800B42563EACC3F8D48A9 B73C34564F06849DC708E5E77E5A06140BA3A0844AB953ECD631491F0209454B EE029720A190E35F9E423E614EA07329CE79C537E726FB7611DAD5742CFB2C15 EF584B60D6BFDA20586D3325B952B0EB87B7B33EF3955C39273D60194F32231F 9C66E0E33752483AD32B626BA81EFF52B083240A59BB18EA43E4D81AB79C0B66 5309663F60BDF6CA8CD593E9DE67861A3A2B61839585C4CEB047276395488F84 9E0AC9DFC39D11944D96611ACF497244D20FF6592DFFCC3B260808E0E4EF60BE 037AC3280175B42A06CFA47D437757EA879E24790FE0663173CD01217CBF9F39 6372FE2419E4E2FD7C0596037A970FC9AEC7CE10EAC15418A9380D31A71E2407 85739DC41A386B4730EE7E769413660BDFC8F58D7FB49A37DEA89DC8BAEA4140 919A76680638724076F54A36B3344CCFC6CD4AE80DF6F5E02F88B2E2BFECEB55 5571D696769DD59F59E06436809AB443401850CE4C76184B417F92DD054131CF D1E05F74B17E73132D1D2CC0E0CE462353C46341AD8C69FF2EB48F0E6AB01916 040CDDE7AA26F2817C80538A865012B8CB71ECE5E7C893A2FD62259457BF3EB0 1540ABCA857C430FB682FC60DBC4FCA9816CB75D1CA853887FE3E4B2C835206B DB65F9B19FF798430B188B0AB383762AFBD33F9C31DAEDD5AB8E1CD2B44586C8 4D01123B58DFC901CA5853A7023C0C006D6C7A4A4A5D4777E35BDBE464D2BDE8 39C57FC38A7BA068C99A6A6DCE4D47FD2A98AE5CE64260937099583FC1AB0232 4349B1EA1CA1860665CF38D5838E1921777AFD5D54BADC28AEA4776107F4523C EFB382EA40BD12B4614F336567C318E4A4D56147BDBC655FD0CF2EF0B833B10D 9C80871B919CDBCE6C86FC46A9E4EB5588D6520393382F67EDE36474BB272B65 86C0D285978474F432EE0353014499BA79BA018688B732DB04A0F1DCAF12E867 A8D36EE2AD7FEC75E4DEF6E24957CA43E7A0ACB40338F74FAA6BCC5D13C963D3 07A09F94D93CFF16523ACB85F88375ABC44D146D000932153D5C0D2C7C6F52D6 434B26BDCF7BD150212F0A86063D675C3922DAAAB31084DBBD64325738A79CF9 4D64FB3480228C1F42F9F8D07CA2F71471B48F898C6B348684C2718EC134A744 A540BF0D3B9C6C98FC87A723286E28A18FFF5548D2DDA225CA9ACF722BB23293 38FD5AD99B5859D4D8D65DF79626D82BE6870B0F09D27A6FBE1663B57A79CF95 81AE0D75AE2EFF7E9AB37F85C7A134CB117D7BF9252FC210DB853E4E41861471 1C4C7FCFC613DC55A1F071E83676E56DA9B02CFA84F13EA2E0A1D84654797A21 7EDD2D0FB9A7E294EE43E639966D82FA3240A56B4E308BAE99882FB5D50CA234 1B4E14E875306C6A305EE0254A3785015167FBE12889306269FBD7E39E66CBD0 2F3C18AC482EFBD479CE029FCB5C1241BD47FBD36157CD9B97ED3448B664835F 5C7E79F7F7AEACC339183E99BE412EE2FEB6B1483A71FE048FDB0FEA9D0ECE39 A0D0219766999D4A1A5773E0BE6531B8D14C7DA3B893F4E3B815FA4A7144F944 08D63F2F2D6F2AAC78BEB1A632489FAA35A5F2FDCB7272F60F6A771A7BA81835 24DB266C86D1B61EF3B919952C360D88699CB04FC3438AAC8171016B1F589F71 EBDE6DD9AA01EEF63ACD3B941EA7261846AFE9B3B66DC241D874A3895AD0C23D FBE9BD890E5DEE1EAE0F0FEF2BAE2AFFD22427DC24BB71E14A50769163E82260 1A6DFD4E7F517271F815CBD5BBFD84C7628D736B8AC90C6B508D7680E805AFE8 88920FA2B4BC8A1A7D24FAA48D3A54EBCECEB97216F3F95AABF81B747F630AF7 99F629D4E8F07FC31902BA8284CBB54340749E22AC3E4F8E4CCF8B1CC106A24A E099C79CF286CE646AE8F29917FCA6D11527CEB2C7861B9CA901A50EC89957D8 1158DF44F715138E1C6F4598C581EDF39528AB4B2867D230BD1421E75C8754A7 9E2E3BAF8038C053570F25EF0B3BAB8380F6E4760AC8CDD38D1EA79959CBE64C A90B7A63AB4EC38AA16EBB5D39C6BAA23630A1A98DD3D2533DA8D2BA58804B1A 81DA9AD0A0B02C805E0193C9A46B965B49B76815300ABECC280FF7A6E27D1014 87E759E72F7ADD2C49E0A7CD53DC748E4AA3D9A3F2724D5A3DA33C64BE4E91F0 B794E80949BECD01FD3B1DA67E1BB00F2D49704C847B63C8D5C5DE9F553F68E1 4A765FDDDD6A2404922AEC2238D70934777742182BE4E74163928D7F53BD2E62 A4B09CA4A79E83E5F57F4FBD490905ED1254DB57B290748AE1EFB43563F20C8B FC801255A97AFC361DCBA6B7133D7FF35E7E21ECED1FB3CBF7A1BC9A209C7704 9E7F83C83764B4FF0D7DCB685BC90B3E95039BC0F3072710E45193AE6464D655 43446199FE4363D5353FE7556B65FB6E5200EC311F9D9CB3355791AFFD2471B1 B07813598079C806484F08464C79106B628F53D3C2EB3BCA5D1471A063D092CC 9C1D83FB531CE8F4CB9D384A40CCA0127392DE88FE2750F81FBCB09DD8E3A511 68A917D815E3304C7D60ECA349C1759AFB00BE1AEC52D944CE914A6CE0000CC5 ABAC4DCD6896E6E20F8A65D068EDBAC8694216D11A9632D95373A06216920719 C433DCD866AFCBFD54DA97CCE55BEBC17A68E60B217334C2B9EF116E7589234A D0E7D7DE0C267626D58BC3B70718A8CC492E3B8D31FD48C9A2552D70F97785D5 BDF4548775CFD848569702F330732E00A755A0DF594A1E1A92A40450B14C0CDF C401E0F714761BA56A1777CCA3AC66B1C43B465EAE732DFFEFFA23B183F7E29A 8105AA7789E87424C6067E3A48037C39F82C3B1EE8F4D07A1E7BC221FC9ACCBE 6F2F289181307BEC470A721E821B03B7BA36C969A6D552690C4DACDBA8E45CF5 E589BB5801CD107428675CDF8099E9CC59064EFA273526451F8E04974B2FC1D0 316C073A8ACF54EB44408F6CAD5B6E9616E4AE1C2658E4344BF4ABA0270912F6 77E8C91037DD856CFB1B497ADE32719DC2C2DD7ABFD3831340A8DB260FD639FF DA11E3E7FA5970C3FC1F2508D4A42B965AA37A6329AA2764BA11A46CCA5AD738 DC36652906E3647E8BA203718BF90FA3A9A4EF31B74451042D5D9ABD0CD9373D B3F3D173B5E2E701B975BB5D913D1BEFCF1347B9E070FD1236456740209A929D 39A52AC2A7B87E3D97DBF4E5EB1AF6541FBEF1850DB693A5DD84DFFF26D37210 217241369BA4E0C0ED35348637FB49703D32B6D53BF842CEE6E5C33059A046B4 F49E3C2461B7072F3D68CAC3A5558104EE96ACEE15917AF9DBEF183F4886BD9C 3C3CE8360F0AA233AE6836B7668D6CA8ABA1FA72B97C2C0EBD123B1A66B8E4EB F6C903A554292A34E7EB12B3ECB25A23097C17D8987BB5626C020ABC5525A28E 6C47FD172746B2135DAC5ED0DDBC3A4B0CE9997688EE7F2A7EEBECB13AB104E2 5A7E3757DC6E739FB277E8F7A475ECD4DF601CE349F3769DAD5BE0E65F5C9F82 7FBAB22A62369F7C5B3E1E812357A72EBEB36AA7CDC8FE012C06E20B5C1EC457 4D81B5D9F0AC05C8FB83AD836DDACE2D5F2323A9C7D11CFB01704661C1020D34 2D698866C6DF99E1F33FCCBEF60CC09DD3E5689A41E18E7D9EF0668533141662 13C7AC5FA32E678B18C4DEF871CCC3E740F7EC92CC7467F5EE3A72A3CA8D1CBA 00E94A55BA750F16A930DE7A29D8731ABC90EC57C71AB2F4792C48A3F5A3EB70 D33E3174015BAF645C8C91A58FDDF641F8E71035D15ECB307FD1EDF7BFFE0263 FDF179DE281E0F6470B6969FD2CA2AC47E65896CF5A1D2F3C5CE837EECCD8886 F119B75D7887DC907249541051E6AD0CE96513D0F5703887410E65275182CED5 DDB4855FFECA717DA351A4543B598482976B017FC37F2A8A3385285DBB0ACF3C ECD38E9514264B69DBF4F524A1163EFC7E9E96D1072A6DA986970C1EDF6258CA FE0206A933449003F43F7FF904BED3883CE7C33EE1BD326DA3608708D0020DDA 7FE03336CCC2B33244DE4AF0AE01B8E35C720025E9B860C0C508CE201FA8CBCA 12CB4CEF4BD5EC3C72B9C57D5A80438FCF2B4AE2FD46EBCF1C46579975E04102 AD42F7B669D110E82B58916C90BD3FC63F841887159D6A59573E1FD7224E4235 F45B459D0C8D92C087DCC83DE7F7EA3A386C5CF50E78AAD3E80E8D012BFFD120 E6BDBD8E5EFFAA08DFFEFB1505808884FDF2D845DA677989C24F8F4007E8B7D7 CAC5C4E9761209BDAA29B30D5A72DF84DBA041A71A4852E133B5FB79196B99F6 6E0E5F8F738868F00B89DEE7A31EA283B69AC2179E3938563BDDD71380363CEC E99B4D27157430F5F0CBCD2114608F2BE0529C62C967A9F6E58B3521B9DB3C30 10B5456A47737915097FE618F745D3414A330E476093F11A926114C1FAB6EA53 1FEAB8A06040F14D25B642D018A7538207090214C91D1F5142BC8B57B3D55694 ECB383789EC4E2E4BD40A260F4A74AE2C1C929BA31BD26A5B0C5E582897F9213 DD0D35643893DF36D8FEEBEED584FDDA3FEFC9716C3A636D0BA3893A103F79EC ADC177DE475929CBBD11C5FD9B8B9F7B791268B1A05C7FDB0205A3717AF24108 20B9DED61354BBF61E230471AC1205F86A0B6EB918AFE13C5209D9FAD39F6EF3 6F4FF43292963FB155CE3E6CF782C268722F17746441CEABAB4E35653D7650AD 2AE645E2779964703312D6937A83C29DFA2D58ED9DAA22650F061F50D17FA701 113489421BB77F7CDB098E17ACC8E2D3B803455E43917F9451724884DD95CD0E 7994FAC00B33E343B34ECF45AF537915B9A30D6DF78108FB8E6E84897674C64C C7DB96E4C792822DDA554C809FBCBE0DD7DBD3C0687CC6ED6C4437B07182E57A 2FD389B64B26C773CBD4283FE78D4ED080BA9FA5EDA7F65EF4F964FDBA6F8CFF 5818D1144FD0B80E507AACC72A08189E6C14D66133BC1196A728ECEF9F5A19AA A4E78E5CF56316E1003F0968DE67387CE4863A6D36F76EF04B7B4F41E0D3E607 4863EDB5BB871490FD03A984A08D4FDC9BB40C51F2D4E7F33B26DB2F1A34B838 85E5592B8D044EB66A64FFB810079CAFD05B226B84DAC44FA3F0B2E10354C270 92579596B5BE62BA33CA4E91092FDA394A272BC3CFD1EE53D8BDFEA26D637FED 6F2A9C26E20258A3608C75A1CBD2F8B29DA5159BB75A7EFD9945851615D2E385 62A699817AD4E656704F6242CD707CE09FD90FACF4283B0E7FAE88E8668930DD 5697514F333751F9F7E450A5D5D024300E4389725C1DBB76E732021FC30B4E7D 99B4A261A9B967386E8EDAD3E1D0C82E553CED8276352DA299901027B94C5B9D 60822BA273CD3DBFFA305F06AC2DF5C1BF74BA922FF6F02423FD6DACA9E6D324 94C3789208AC8C736FBE23539437876E8D1ED16E9E72FC8902F96EAD1837EA31 E069B227F2EE2D93016C0BFBC14DEA3189F30655538F264FDA963F7C61116077 9F3A32655B330EE4322AAE431111870BA9DF3F91CB0BBB84A68884FC195E31EC 06EC46805472A7D7569576AC7ACBD18BC87DAC66F2B14D5BCA7470313B323338 6EB51833EA2215370459A6EDDF6A014EFEDE2F35783094DA216B7315778FB3F8 A55752C7D69C3ED23A164E53EC3B9F2DBB78EB306A971B64C7CEF60C0D1FCF07 7EEB24950656E7FC18C530C1E136661A25D55C99ABC2574F771D8987A0E8AF27 EDA41AA55B4547817A297B148D8BF857F75136D0E3576156AA6291395F61AD32 07786D0B44EE11E762EDE7782EF2301984033950C8CEFFF9FA917017DA4C6FE0 2C8D5494767180F0D85C4713B9966A68659F7E908D7AD785A0CEB17F8053A955 3550A225700A4B2AFA27E89F4AF23384E7DFBADA4D6D4353B360DE26EC397E13 08F7540F358363EBA53C4A2EE8D576793A1002A4E56C6CF955C6F928784C8B04 677BDF672BE43429F633EE054C0CC80ACBE77F4A7726E6DBA80CEAD49B1FCFC2 60B4A901C920D892A0BA5E1BA3CE3968E6A081D336159C3C48F97C8C5CE6985B B157417557860FBC6E4D2C7D2415238E80BF1975B46F8544BA790637B74D2E84 229389F2DC762F794FAB3404C3530CF567856F757E785A7620118ECF766B5B0C B3703080609A3B650AE2AE1B72ED498FC472A1D267B3D515F58F116B92986A06 DED0FCC76137BAE7B39A4E4EFB3128326448ED20FF1C3CB23901BE14460AC212 ECA3F65C7F6D231C77D2E98BBADCA935D50BA0E08AFD08F7026F6C42DCD904B3 804BE0A769550F82BFFC86F0A8DA60527C6DF98FA98707F828DBC4ADEC6BAD78 B129E41805BC702D42CFF597D093C833D81CC64EA31CEB25B39FCED202E36563 81231D4877A1B4D8EA222D71EFD972FC6BFC0064AE2E20FDF29823590E9EF64B CA1E6C0DA7DFA2756967CF0D205F9947083D7341C8AAA39856130475F13CA879 FD9324C56726A31441D0FAFD92C99DF85B331A4047BE8A314105E06D85A70271 3FEEA1412A1DA9625AA1FC7E13822D61C458C5FF10B20419DCD965764D9D436E 6FAE3D237D42A572B50541EC1C34526D16339D0EA4124131C4868CB0153A3489 B6A8F662238A23EFEFCC0DF613FECAE20546DDCB6E87933CB9F91EA21E0FD502 26E10CA34EEAC50C6E5869D4013E2E9713E220FD7B6355CF94653A583DA3806D 24A516C196A293062460870E465CDB74C55CACC2CF0275BF84832578DF676456 7DE79FAA30DC3F3BFEA86F75B247899093CAF82124F280E446BD6B8D00CCF6F5 93C2659521CF0F481AD3B49DA55E96448345C1C63CC00B9E36BD77ACBE575253 BBF3C5390E993D2357C8FA61359CE213BB7C484404987AAD9B6396A9286FC09F 84DDEC1B63ADF316B028D67728264D932B964930E83CC29957AD480B9FC244F4 7D18D655490C9BCADB1182193C4856790215E8811DF0B937FDF5BD15663BAD7C 9FA7E25DE87D46A7F16C29232CA8B4D89FE29866D94DAC106C68C1DF3A4AA9A0 F1B0C0E549F0B8F4E45D601D3BA784450FF133AED1757BFD5FCD20EA66CA4EBF 1219FF566AD332763D3B30B96D39828E42616E5B9BF3294D976D3A3F0C041115 4873F736A944C1B4D17D2DAACC0CDB25D0A2909642DE9F7F5AD73CFBFB3F27CA 35D19A912BF578B25DE160F3A8B89CF5317BE6607E13030FF2747B15604B93D1 4A0BA704145A30FAF37136318D61257A394E022068088E15B7F4AFE5DE87D818 FB6C60BABA376A01B8A943C2B924E68ACB733DD49E14F5D2034DD87BE83C943B 3A9A7728CE2378DC489A233A8F786130D6CE87AFF83D4CEC24B2F42F9C4A4FD1 B8F6BF8294A654381F568F1A9BE91D883E22DF40319041FFCAF8FFB770C17ED5 7AA2323B0EF7AD80CD5F7B91235E4B3C54A360108FF786541CAAEA02FB002F50 3859E01F88396D8320D8AED134B831697A08CBC5FE104162D110E60110192CF2 32FAF106B1BA9A15D106E8612D0846D5E01EFEDDDD0733C3CD7176F612A7F702 C0EB49639CA54B5D20CAC1FE519582915C19E6D4F7EA59A80629FFE47025364A 25665FAFDD666B9387A27FF02D478AC425AC1E52C8899B8FCCB1A3AC99B8872B 11552D5CFC44A4D051FA0AFB81F11A4B64504F9DD5B3E615715BA17E5F783FB4 D2A300AA7C3EBF6BA7079D20D4117B66E84CF0DD95A2A5484B076C7B902B7994 779D53145BCE458F6B344EB4E668C53BA6F69627F9E9B43EEC3A936B1583F535 3F237362CB027E3E24D846405C6BC8ADCF670D14D1AD97C1CB4BB0BF740869F9 7B9F3F7D41B9CD078AEB56D92C298DB57110248EC7DEED9A787E107C119E445F 99D34C52F09F130FAF99C3C1A7462C0BE606CAD0FA0280E8993ADE61695EEF0F 13E50DD90429A35DF4449E15747A110C072161F8CC06F249F2716BE04995139B C6019C5716C946478CDC70E90A60B7A0463843590B841E67045C4783B0436857 DA50727A1280431B9ABC9B3DF39867425E1B39103A1DEE9FEB41C852E0E96A38 213D5E7820576E36B9F220FA1EBCA805AC979D32E1F94AB749C13AC640F20334 86A959FD654577B4F51090867CF6867AE826FDEFD65FA2B04C522C3F5AFA65B6 0E5CAE2204D0CDD0115B4A742521EAF088244194682FFC131AF8EF12C3DDCF0C 85B85E4B2EC21B57DFA73F271E0990996796D865EFE6A30D2470C3676A9E1412 3759984F19C6C209E4A7AB14377F16473F7F72DD511E4A329AB63CE368C742A9 496CDF68E1C90128BFB134E30DB02A120BF3C54B504297174AAFA94FB8731DA8 BA06EFBA37F2940759BF534B002DBEFF22070A6A6045CEFF58ADD7C2557AC247 E7D6BA4D350626B688E5CDB3873DB43279A5589DEEB33700A5D5FE7A97C4F779 A8F1C8FB0B560D07960BED9F5E881E45205C363E578517300038093A0E05A4F1 5160853EA6A073CBEC6E662AD6A11D67FFB10E678CC79E36303DD725A330BF9E EFE118B61E6CD98F45CB101D6A58B5B299B0B8AB9EA70804891F237E07D494B5 72F9CD0133189B914E0662F376A48E149D847976996414D95AA453798B51B882 D1C833E15FC5801BA78FDA8939E83CFC021277F1507F93C3BFCF03E21CCAC7D8 BEA7A22E17C868C3E77C77EBF96ADA44655E55FFF6ADD7FBF49E890B6D5329AC 98BB13E8E3A9D667B17CDB35A8EB3B15AF4002159ACD8A08304C3B21D8208C92 9F95B4D0AC3BDBFE935434BD788E47A8ECDB48617796C52AC5CD6AA8972CEAD3 B33BCA75820BBE5A8FA11A10565933C0DFD564531C7ADB551E584AC8B1D0F740 D776FA13C6CCCB3E71761345D8A151D08DF0705E55646DC44A90214EC9609027 72AE7D24C4E1E7916CC2ECF3EB7563EC99 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 14 /ffi put dup 39 /quoteright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 124 /emdash put dup 127 /dieresis put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 61 /slash put dup 65 /A put dup 66 /B put dup 78 /N put dup 80 /P put dup 110 /n put dup 116 /t put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D6F5CA5FED4F9AC9ADE41E04F9FC52E758C9F45A92BED935 86F9CFDB57732045913A6422AD4206418610C81D882EE493DE9523CC1BFE1505 DD1390B19BC1947A01B93BC668BE9B2A0E69A968554239B88C00AF9FBDF09CCD 67D3B2094C11A04762FE8CC1E91D020A28B3C122D24BEAACF82313F4604F2FEF 6E176D730A879BE45DD0D4996EF0247AEB1CA0AB08FF374D99F06D47B36F9554 FAD9A2D3CE451B7791C3709D8A1DDDEFBD840C1B42AB824D5A0DFF0E0F15B0B7 22AEEB877FF489581DA6FA8DA64944555101EB16F7AB0B717E148B7B98D8DBFD 730C52937E226545CF8DC3E07C5BA30739BAFCD0F2B44275A6D503F582C0FB4F 449963D0AD2FAFDE33BA3D77BCA9D1DF878DDAFCA2E22CC4BACD542B282164C7 97C2BDE318AF9D501CA21F6E662E7AAB75A5F24D2C182E598D175D44E88AB19A E7CD59584F95B389183EE21B525BF52A3F23C0FE5383A5565A19361D716F508C AAB78411CA5A4D27552CC1C435760D5A89D535B71C593E755C616661363308DA A683F54ED0C23FB2C225A008392B0B719F66F11A946A090B7C00B662A3C69599 B4ECB0CC70C85C4BBBF207E0026F6C7A19F2ACFB7A60804FC98A4BFFD7BFFF2B 9529E6D9D4238002BBC255BC62959D6F3381FE06E0621B879D5FE5B541D45A1E 759A6E7DC32B1D1632368D09A97039DF255B6492B1B2B7E2C1434E8306ECA7D3 5A79B6D614B4979F10988BC76ED53A5F45315CD7DA216221F842FD0F3E050DD2 BAC23C984D506D8F7D614BCB6B244F5F41321549BB0BD041FBF3053307168680 3435E9C94EAAA370BDC38451CC8667BD00C4D71F79F9A557DDFC76E4B75BC4D9 83DDFD0AAA0124B4C54B43F53901F2CA672E40896157AA531EE4EB1CC24BF186 B31EE2521304106808EC781730279CAFE4FDFF044BAD177A375757E7BB30A754 8AE63401487032E24DB383034BCC13390B873D0BBE235051957EFA5E6093B6C7 6EB6AB852A640AE29229719EF12F5E0950F854230CA24936E081A25F4F19DD87 8AC3A7AAB4B34884FAB3ABC36F3F72DD040440AEC0D23DB4987F87E3691F5147 62E4043A26439CA5966887EDE760AEDC2AD4BDB9857019877DFE1D4AF0E5FCF2 1B11AC9B4C8B08538F0912E4F17AF28E81692F75FE504991BFD3CD6716A65CF5 EA6302D637F895FDFFF4A97C1AD9211DDE1751AD5E06937CBB6CD50621155888 203AFCA27C8A9B8459646072136038F051B80EF4DDECBFA79CEEE0BC3E95C10F 4D10A4CA3FA871CF876D92B6A3A33A5B25DFE84F4CD0FF356813D340AE07E0FF FB0B7857BF7E0AC0F3E946A70663372689B9043611641DC092DA9152670B55DE 5E3624A7FD6C125EB45AF2CDACDDA9CBF763293E5E6E761430BBB06CE041A2A5 36493281502A96186D2D1A012CCCD83C72683A371B5FDEF20477B5822A8B341B 7D119229CFE9A910BE35D3412F09976CD096151E87E282B5BFBE7071324BBE32 41B41F765F45AB6882F424A485183144A76054DFCCE75684A09A4EF9FCF53741 04EBCBDDBE56A7AF76A9A8CB9D3CA933A0DA3DD463AE6569FF8A2591B866C086 38742C119B88B00130A591755286F60D41838F86E3644D99796D257A035D3E9B D21493EAFA196811E4494D0A04D3A3F5BED31A94D51ED5FB45024CDE7B62CD12 45637E8EA2A9F430355F81485D3B720F4B904590EF3AF4084BCEFFB0D437D501 9DBF379F9269414BD39C6981BE6541916646AD6B968C469A955554203691EAD6 9E617A300C4C526C23A99D8451D84AFB98844CC256BD716CAB738BAD91870C45 5F2BD1AA996C8468CEFC4EDDB86EA25074F7968356FF35EC83C4F3DA387DB512 ECE9091646AA1EAD51FE73CDC17BC8D5315C6EE3007E13CD3180878D09FD4FB0 4E9787835A90BF360948942435E73B53FB1BFB8B6DA768692368718B54B8A62E 0394C948653823ADD7CA0F384B7D8C697ED16281428FAAD8FBA7309F41EADE70 69E4C100CD85DCD5E2E68977200568A09E73B94EC14B1761D25B61956A200120 4C9A1D02EF613DEDAB32DA00EB608789DE06FDBD426390D7A325B7BC0300EE38 6E74B0035E0C54DB991CAA63E86450CF506A4B53D6D2AE0C0F9299E3F9C59300 9A38B1622E9F278A8D2138E67E80F98D6151DAA5D99B17CF374EF3DB2257ED53 57FD521D6F20FBA81ED0A9B815F480EEB3835083C21352CB88D3781280ECDCEC 0EFBB18DF95A9E6C2D8FE0A8955F21CEF0FD6B63F7C758975D066202E682790F 3B24F9337FE61A2DC1B25AC929DD157C4FAA973431F5CBD771260D11B5917B0B 4E12C7AB5CD8A5CDCB306DE9BD1F6852B80012592E61842AC3F055A6BB48DE40 AD90550118D8490E6ED1ABEFDD9108A278C6916ED7DC4472BECFEB6C100FBEF2 709137693CFF7FE73398A479AD0E1E12DB4B828CD8C6C3657A3A0F5AE1C24138 CFEEF3FB128EE61D6707A6F6767DC53FCB4BBCDCAC8D4FF9208C88F5C71A5721 F66548534290DE827C4668294EDAACE32403CBCE4FC3021120083DEC767A6333 877B70DA101BA9C4A17C519DFD412514B3E9653DDEA9C2187D3A8DF106BBE482 1DF2B53E0714BBAC0F1172F956E28789C179BDB2E9B0456BD3C79D5387823CB7 65B182C194E0863C0199610F26FF7F2F64CF481D9F627570E5F726BD7DD4B074 1C868956B248F8DA15958A02935E90FE319043D7C37AD2B4CFFB736686C9FB65 39C07408A94A40DEC4D3394B10801ABC33AA85F2B75377A4D368C0F7258DA036 F77B329EE9934E059B2A95A6D1B4F98AFD65EFBAB4C46925421D36DC0F5F9680 73D89DC4109C1C7528EF1E2E5354EA4FA7B3E5FC1180C9D504FEEBAE209C9679 23B1B5126B4A58E73222167E81B058F04A88C365AB8CD21138BBB0BED368E641 1E30BDB341C22D77DD7E661EAF35DAB27A0511E72CF49083D24B04AF088ACFB2 8565BA132F01FA843F12B25D31FC4392DD4CDDFFC3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSS9 %!PS-AdobeFont-1.1: CMSS9 1.0 %%CreationDate: 1991 Aug 20 17:34:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 78 /N put dup 80 /P put dup 81 /Q put dup 83 /S put dup 84 /T put dup 99 /c put dup 108 /l put dup 111 /o put dup 112 /p put dup 121 /y put readonly def /FontBBox{-63 -250 1027 760}readonly def /UniqueID 5000802 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 8 /Phi put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 124 /emdash put dup 127 /dieresis put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 103 /g put dup 108 /l put dup 111 /o put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 6 /Sigma put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 88 /X put dup 97 /a put dup 99 /c put dup 101 /e put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 121 /y put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /Lambda put dup 5 /Pi put dup 6 /Sigma put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 16 /dotlessi put dup 19 /acute put dup 20 /caron put dup 23 /ring put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 103 /g put dup 108 /l put dup 111 /o put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA1772CE422BB1D7283AD675B65 48A7EA0069A883EC1DAA3E1F9ECE7586D6CF0A128CD557C7E5D7AA3EA97EBAD3 9619D1BFCF4A6D64768741EDEA0A5B0EFBBF347CDCBE2E03D756967A16B613DB 0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB 8AB317333110531E5C44A4CB4B5ACD571A1A60960B15E450948A5EEA14DD330F EA209265DB8E1A1FC80DCD3860323FD26C113B041A88C88A21655878680A4466 FA10403D24BB97152A49B842C180E4D258C9D48F21D057782D90623116830BA3 9902B3C5F2F2DD01433B0D7099C07DBDE268D0FFED5169BCD03D48B2F058AD62 D8678C626DC7A3F352152C99BA963EF95F8AD11DB8B0D351210A17E4C2C55AD8 9EB64172935D3C20A398F3EEEEC31551966A7438EF3FEE422C6D4E05337620D5 ACC7B52BED984BFAAD36EF9D20748B05D07BE4414A63975125D272FAD83F76E6 10FFF8363014BE526D580873C5A42B70FA911EC7B86905F13AFE55EB0273F582 83158793B8CC296B8DE1DCCF1250FD57CB0E035C7EDA3B0092ED940D37A05493 2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA901C077A059F709F30 4384CB5FA748F2054FAD9A7A43D4EA427918BD414F766531136B60C3477C6632 BEFE3897B58C19276A301926C2AEF2756B367319772C9B201C49B4D935A8267B 041D6F1783B6AEA4DAC4F5B3507D7032AA640AAB12E343A4E9BDCF419C04A721 3888B25AF4E293AACED9A6BDC78E61DA1C424C6503CC1885F762BADBF392C7F6 73B64A75DB0DEC7E63389ABA9AEAB9486DF4C27F5D89D49EE48922899CB186B2 00566A8322021EB46EC015FBC2B7F6C07968728AC8AA7440748E86AF74185FC2 CEC8364F01752EFAD49697D46AD05E5B9E7F694B26A56799A520479919EAE480 811F374A2A16CE8C779CFCDBE29CECBBD4150D8F1FA0C00C0ECE07638FCD5737 7C6D783D32A751F9845398F87C72097C1A618D170DD44FE4AD746C2D25F4EA8C BECD208C1F0D83F8FA0BE68EB6E224BB60667A2190EC5458D924E29C245AEEA2 21A071C61E5DB71FD0640718151AD17E654E2763189E98EDAA41EBAA99939999 C61FC0AED863E5D700C3130958B46CA01D9BBE39FAF9E0EF9181746C63364E36 C43E848CD143A53ECB1E04D9765E822010BD67CFBB484E133B06C219609AD561 BEBD73239C3516D7E5707BC700C352F05FD32AF4FDEBEDB16A867CF8811AB59F 94006FE8BE7B2BC17A3C37779D3020F4F240B2C72A5BA94C8FBEE36531DFDDC9 F7A45C869A236F94E35C1CA80A9668FFA3356E725E22D09A3055B8A9EFF9C57D C15EE257CE4A777805D512DEA45070AF48FB90760E30D34569EC181D9FDD7B32 5045EC58C7696D23BFF84A397565DADA5FF0CD91F1EE856097C6E6CFE6F31CCA 85B1AFB47ADFECE08BCD30CDBFEFBAE13FF73A29819D9B8E234067900DDDFFC1 47C171A3D1A1F9B33F69DB3DE5E88564C20426774D3F37DEEF7241AB98BF7CF3 FCFF389F74108FA74CF246BD6900EECB26EE724F1004CFC1EE4AAA79A6774401 7D5FC0BEDDA17AF34A3CA155D33C95861D7AB3AEBF744351562AD66136FD7AF3 830B210C290BA48BE9D9812AC6A81DC6DBE45D19F0F7BF836C96A4E611145201 2F021ACD05CE5D7B6409EC53A7E06E56E13580076D242E350CEC78C5C9094659 F5B1217D864A366F6D12A5EE4229EC022783E152781F75F9B410810D218E2438 9C79BE24A6D6F1EB9D39565882D297F9F372B187AAFA94F32A358FB1213FE03B 95444475D62F01A011B66EB26A928C0B16FD734464D69FA0DDBCB46EC11E9815 E350773528951B7FAD283D52232EE16295198305CCE81FB0CBCA4D72251ED487 246F87AB83DACF52AC5E00D9ED7C35E69796267BF1F5CA936BADC7275C479B97 5379ACEC6B55656A72316CA5A4FB275825E0AB3120C4FE96A0706DC6C1E769A8 684A5D17C18A0BD1EC6566ECA676DF34E6EB1E8752667140E56543DE979A7362 457277F11BB2F5C99190822FD04570BDF20B09456FB94B7EB437CD1BA964BDC7 8581CF9A2612561C4B22AED0777EDD54614C2A55F8F2FCD667420DB3E6404404 3E284FADAFA08F913E155C11474C651CD2EFD1114DFA49EA502464F04FB04CCC C261781A7F95B919462D9A907BDBCF87CF763F58E9E237E180370B45A9A79CAD 7308BDA7CA1CED7710006982A571CA6A83C3C1013995835C634D9AA024FD0FB3 C83FB564DE7C04F5807AE0B034F3C4578BABC9CE9EE2CF68D7AC854764826944 13BBC35BD61E005AAAF916959F7B679FC658FEBFEF15A368D9E4BBDA534AA675 8C01DC4225A3DC4177BD35CF3C24D990F6CECA070458C7DB01C4B4F3528BC439 3217D02560C2D19789ABB0EE8CEEF27E8C9AB86E01BB53DC1A8061F761532C9F A82C2FCFC48544AC292E7205A5751D65F6C52FE0A7CBE5F574FCF3FEFA119695 4FFC52905A67C7D0A2F3EF821007FBE238F5979898F3F9E0FE27676350154F8A 5031338F04F609CCEE62DEC42DCFBB101D9F0DBD988DB90E7DC0BD3C11D72734 A15E4B1F0B69027A1D836147B3E717203AA4B7115F70247633D112BE9E5834DF 779E8B4577F34DE516E9BCDF412DADD0EA42F9A4897A188FC6BFC6067C9C266A 054E50C8C852AE70C53D6B6C211AFC3FD50BB00512117D5FAF80DD2BA22DFFF5 E9980572517B12416C70CBFDDFAE5A516A6194564746655B7F1A62D036C43210 9090F6C5EE6F97623ECFC88A697FDFBFF96701E2B28791E59606FBD65A40A7FD 8419BAED17C568CF14C8B636D791E20FCE2610689BB41665D072ED83DB9910B8 A0B2288499B4636B7A385B1DF48DEA0B644C6CBD88CA59840D7A49D8677DD670 449D6C8377CC71926DB0411ED604528513484589CA303174E08DF7F25915F42C 0E8BCC82298B089FE0F00E020B77B12C4A5760E9A6CF7710B2755C9187D5997F 7517F9C306FECDBDEF0F077E03294141368386BCFAF78F79A705E778E246D293 E765DEA02702CAB240C50B77B29AEF716E84D37345C8BC9A2CBB76A03A3D896B 37C6BE3CB15A0A371845710A9151C028A7C7FBD2BAFFE9E687990503763D972C D743F0CF5FFD66C4281B438B86B40A3DB82D1D2E525D6C80C02F54423E27A004 28F9EB917BDBC81871F1F86B96C91DA09FD1172E8DE191D5C20F9EAF7AE4DC50 D069E3F2DDD078FF41CFEC131A016E3F86ADBA08C5319B0725330696F18540A5 35F13D03FA7884318343797FF21CC47694BCBC85FA96E4EA83E27AB435F5F484 7DA62D9AA777C9FE47246BC298D64F5DA9C4AFC2B189FA079B10422E2BEEFB89 F1D4340AABC7E16C672F5D5BB5D99E30E5338E5E630F836AC779D8C4939F0F9E ED90DA2FCBA3E643FACE946273B1533BD51418A6CAA2ABE8C22F21FA684FC600 F9B49D6D9DBB9D69CDDB7DCEB53A1AA193EE77CCD1CB529772C8A305FFC01CBA C2AE8CA577590A6EC0C3874E1A2D1E72FC3C8F9B78E17E1F4A91BC363C016287 CDF7912D9A79407727048FCEC7F13EFE0DE8D54AA70028179A9EEA844A93179F ED8CF72AFB2CBB72A71F21FD1403F9AB1176EBDB54039AB0B1B505EB79C3C3C7 864FA1454013F2335D1A0F5B9C113FA67926EA679B3682BFECC82906024BBD7B FB12E651AA17CB65C4CB67474507835F55DD5DC5EB4C9107375D642FAB057A79 77DDF9083A52AD70D2BCBE412EDC0CE9CEE178EEB5D51E5A8891B7F643191001 BDFFDB36404A45465A4202FE90F3875F1974F32C3F9D4C56948F8C5B2D0857AA 4A9B2376B7AB788A7BA95A931F1F5D4E08026EA1148B3C590509D9CAA70A4B0F AAF23DB26A5C8536A6E96F6270FC8896BC33B3C6ED509EFE6AA526F14BD10AC8 2CF754FF24C74CAA9A21783B4E67E44C1DABA9BE97AC54C7323B4581BE898560 B37F1C75C050AF24D71835DD804597AB9B91C91F616F56DCB699FE89F7F31443 BEF9CA9CDDF951B7629CB8EF034BCE3E829C2ED293A397C1A4485DF5056E7CD6 29385F6D2A5FDDFB701CC6C72EEED1884988C67C3A63D5AF5C1AD582DA22DB70 CEA9C369E6DE9867E7AB105EB1BA540CED4A90953B90CEA2B5CBCCDF8B7FCB58 F0841C989D1A5C8B81D7C34ABA794F6800A664BBCBD9603729017415F1C4B632 112E75A25225C664B3DEF6EFDDCCBAA9E821C81C1FD10E5D779E3765978142FA E8D738B264BA04898F86FD5B6E2B5D5BA9D0C04A2375EF531CC5B5BB99C16C53 CB0C1CA3D47520172153B11FEB85F01B6FFF9059D39107D08016D396C54871DD A8EB39467B8E63F6C9617312B8B5AB8A4F75D0C1C199CD957FF0C23B7773D0E8 9A0DAFB63F90205F6C8611788B72E95E2464F5E6E31D36D82306940248FC3735 24F2AF74100336B2B0EF5C3F40ADFC1323016ACFAE49AE8E6D86F9BB86DBEA60 42687362FC38DC19425BE61D3A27CC38BAF8E8400ACC5256DDADDE9DEC749338 532AA9E4DB39083B42652BD35769A71A60D81EE1A7F478D3EC3BAAC642E8BCDF E9694F9BBF01E75B825E46ADBB3C4702FEA3BCC8E48B8DAD4119C5D70579ACB5 CA6693F17FA2F46195042088A93515D6007EF1023FDE89E22515 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSS17 %!PS-AdobeFont-1.1: CMSS17 1.0 %%CreationDate: 1991 Aug 20 17:33:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 80 /P put readonly def /FontBBox{-58 -250 939 758}readonly def /UniqueID 5000805 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 63 /question put dup 70 /F put dup 73 /I put dup 86 /V put dup 97 /a put dup 100 /d put dup 101 /e put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 39 /quoteright put dup 44 /comma put dup 46 /period put dup 64 /at put dup 80 /P put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec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cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (sep-03.dvi) @start /Fa 140[34 45 4[56 3[23 3[42 20[55 80[{}6 74.7198 /CMCSC10 rf /Fb 243[30 10[42 42{}3 90.9091 /CMEX10 rf /Fc 207[26 48[{}1 49.8132 /CMSS8 rf /Fd 234[48 20[48{}2 49.8132 /CMSY6 rf /Fe 152[38 38 47[0 3[51 50[{}4 74.7198 /CMSY9 rf /Ff 149[20 26[56 57[55 17[35 1[20 55{}6 66.4176 /CMSY8 rf /Fg 145[38 10[28 19[47 17[32 1[19 24[29 34[{}6 49.8132 /CMMI6 rf /Fh 142[45 97[56 15[{}2 90.9091 /MSAM10 rf /Fi 128[52 5[55 55 76 55 58 41 41 43 55 58 52 58 87 29 2[29 58 52 32 48 58 46 58 51 6[64 79 2[79 80 73 58 78 79 71 2[99 63 82 1[40 82 1[66 69 1[76 1[79 6[29 6[52 52 52 2[29 35 3[41 41 27[58 12[{}51 90.9091 /CMBX10 rf /Fj 137[59 62 44 44 46 1[62 56 62 93 31 59 1[31 62 56 34 51 62 50 1[54 9[116 2[78 62 2[77 84 88 4[42 1[88 70 17[56 56 56 56 2[31 37 45[{}34 99.6264 /CMBX12 rf /Fk 167[47 7[45 10[42 69[{}3 66.4176 /CMSS8 rf /Fl 134[37 2[35 41 25 31 32 35 39 39 43 63 20 2[24 39 35 24 35 39 35 1[39 51[27 30[68 14[{}22 74.7198 /CMTI9 rf /Fm 192[71 20[71 42[{}2 90.9091 /MSBM10 rf /Fn 149[25 2[45 45 40 40 40 40 2[61 61 1[61 61 7[55 3[72 8[65 48 1[48 9[51 51 1[0 3[61 8[91 91 6[91 3[91 4[71 2[71 71 1[71 2[45 6[71 5[71 25 71{}33 90.9091 /CMSY10 rf /Fo 133[33 35 40 3[25 5[43 2[37 1[24 41 4[31 15[43 3[54 56 68 48 3[58 1[45 35[33 22[45 11[{}18 66.4176 /CMMI8 rf /Fp 133[42 45 52 65 44 52 33 43 2[46 1[55 80 1[47 4[45 42 47 39 39 48 7[53 75 2[62 1[56 2[58 1[73 88 62 77 2[76 1[58 67 2[69 68 2[71 45 71 25 25 18[59 4[42 11[55 10[58 11[{}41 90.9091 /CMMI10 rf /Fq 128[46 2[93 1[37 44 42 60 42 49 30 37 38 42 46 46 51 74 23 42 28 28 46 42 28 42 46 42 42 46 3[28 1[28 3[91 1[68 65 51 66 1[62 70 68 82 57 1[48 35 68 70 59 62 69 65 64 68 1[46 4[28 46 46 46 46 3[46 46 46 1[28 33 28 4[28 24[80 1[51 12[{}65 90.9091 /CMTI10 rf /Fr 139[28 5[46 29[49 1[61 11[58 58 3[38 61[{}7 74.7198 /CMMI9 rf /Fs 134[35 8[40 38 2[18 8[34 14[52 43 1[57 49 1[54 8[46 1[49 51 51 65[{}14 74.7198 /CMSS9 rf /Ft 128[38 2[77 1[34 41 41 55 41 43 30 30 30 41 43 38 43 64 21 41 23 21 43 38 23 34 43 34 43 38 21 2[21 38 21 47 2[79 58 1[55 43 57 1[52 60 58 70 48 60 1[28 58 60 50 52 59 55 54 58 1[36 1[60 1[21 21 2[38 1[38 38 38 38 38 38 1[21 26 21 2[30 30 21 4[38 21 18[64 1[43 45 2[55 8[{}76 74.7198 /CMR9 rf /Fu 144[30 2[18 4[30 45[30 30 30 30 30 30 30 30 30 30 6[24 24 40[{}15 49.8132 /CMR6 rf /Fv 175[53 1[59 78[{}2 83.022 /CMSS10 rf /Fw 133[37 44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 1[23 46 42 25 37 46 37 46 42 6[51 5[60 46 61 4[76 52 2[30 2[54 1[63 1[59 6[23 12[23 28 23 2[32 32 27[46 12[{}42 83.022 /CMR10 rf /Fx 139[37 38 39 14[42 53 46 31[72 65[{}7 83.022 /CMBX10 rf /Fy 144[35 2[20 4[35 45[35 35 35 35 35 35 35 35 35 35 4[55 1[27 27 40[{}16 66.4176 /CMR8 rf /Fz 175[86 1[95 78[{}2 143.462 /CMSS17 rf /FA 134[70 3[73 51 52 51 1[73 66 73 111 36 6[58 73 2[66 10[99 12[47 2[86 6[62 63[{}17 143.462 /CMR17 rf /FB 134[48 1[48 1[48 48 48 48 48 1[48 48 48 48 48 1[48 48 48 48 48 48 48 48 48 48 15[48 15[48 17[48 1[48 4[48 39[{}27 90.9091 /CMTT10 rf /FC 134[42 8[47 45 47 1[22 6[40 1[40 1[44 8[61 86 2[62 51 59 1[58 67 64 80 49 2[25 64 1[52 54 66 58 1[61 58[66 6[{}26 90.9091 /CMSS10 rf /FD 128[45 45 1[91 45 40 48 48 66 48 51 35 36 36 48 51 45 51 76 25 48 28 25 51 45 28 40 51 40 51 45 25 2[25 45 25 56 68 68 93 68 68 66 51 67 1[62 71 68 83 57 71 47 33 68 71 59 62 69 66 64 68 1[43 1[71 1[25 25 45 45 45 45 45 45 45 45 45 45 45 25 30 25 71 1[35 35 25 3[76 45 25 9[68 2[45 45 2[25 1[76 1[51 53 66 71 66 1[66 68 1[63 3[{}97 90.9091 /CMR10 rf /FE 134[71 71 97 71 75 52 53 55 1[75 67 75 112 37 71 1[37 75 67 41 61 75 60 1[65 12[94 1[100 1[92 1[105 1[81 2[50 2[85 88 1[97 1[102 8[67 67 67 67 67 67 67 67 49[{}40 119.552 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 758 91 a FE(The)45 b(Computational)i(Complexit)l (y)f(Column)1902 317 y FD(b)m(y)1599 543 y FC(Lance)31 b(F)m(ORTNO)m(W)1286 769 y FD(Departmen)m(t)h(of)e(Computer)g(Science) 1520 882 y(Univ)m(ersit)m(y)i(of)e(Chicago)1084 995 y(1100)i(East)f (58th)g(St.,)f(Chicago,)i(IL)e(60637)j(USA)1401 1108 y FB(fortnow@cs.uchicago.edu)1047 1220 y FD(h)m(ttp://www.cs.uc)m (hicago.edu/~fortno)m(w/b)s(eatcs)141 1533 y(I)f(ha)m(v)m(e)h(mo)m(v)m (ed)f(bac)m(k)h(to)f(the)g(Univ)m(ersit)m(y)h(of)f(Chicago)h(and)e(so)h (has)f(the)h(w)m(eb)g(page)g(for)g(this)f(column.)45 b(See)0 1645 y(ab)s(o)m(v)m(e)32 b(for)e(new)g(URL)g(and)g(con)m(tact)i (informaion.)141 1758 y(This)26 b(issue)h(Scott)h(Aaronson)f(writes)f (quite)i(an)e(in)m(teresting)j(\(and)d(opinionated\))i(column)f(on)g (whether)f(the)0 1871 y(P)k(=)g(NP)h(question)f(is)h(indep)s(enden)m(t) e(of)h(the)h(usual)f(axiom)h(systems.)41 b(Enjo)m(y!)830 2296 y FA(Is)i Fz(P)g FA(V)-11 b(ersus)43 b Fz(NP)h FA(F)-11 b(ormally)41 b(Indep)t(enden)l(t?)1623 2508 y FD(Scott)31 b(Aaronson)2237 2475 y Fy(1)1484 2621 y FD(Univ)m(ersit)m(y)g(of)g (California)1452 2734 y(Berk)m(eley)-8 b(,)33 b(California)d(USA)1377 2847 y FB(aaronson@cs.berkeley.edu)1767 3046 y Fx(Abstract)352 3198 y Fw(This)f(is)g(a)g(surv)n(ey)f(ab)r(out)h(the)h(title)g (question,)f(written)g(for)g(p)r(eople)g(who)g(\(lik)n(e)h(the)f (author\))g(see)g(logic)227 3297 y(as)i(forbidding,)g(esoteric,)g(and)g (remote)f(from)h(their)g(usual)g(concerns.)77 b(Beginning)30 b(with)i(a)e(crash)g(course)227 3397 y(on)f(Zermelo-F)-7 b(raenk)n(el)26 b(set)j(theory)-7 b(,)28 b(it)h(discusses)f(oracle)f (indep)r(endence;)k(natural)d(pro)r(ofs;)g(indep)r(endence)227 3497 y(results)h(of)f(Razb)r(oro)n(v,)g(Raz,)h(DeMillo-Lipton,)g (Sazano)n(v,)e(and)i(others;)g(and)f(obstacles)g(to)h(pro)n(ving)f Fv(P)h Fw(vs.)227 3596 y Fv(NP)j Fw(indep)r(enden)n(t)g(of)f(strong)g (logical)f(theories.)79 b(It)32 b(ends)f(with)h(some)f(philosophical)g (m)n(usings)f(on)i(when)227 3696 y(one)27 b(should)h(exp)r(ect)g(a)f (mathematical)g(question)g(to)h(ha)n(v)n(e)e(a)h(de\014nite)i(answ)n (er.)0 3982 y FE(1)135 b(In)l(tro)t(duction)0 4185 y FD(The)42 b FC(P)g FD(vs.)g FC(NP)g FD(problem)g(has)g(b)s(een)f (called)i(\\one)g(of)f(the)h(most)f(imp)s(ortan)m(t)g(problems)g(in)g (con)m(temp)s(orary)0 4298 y(mathematics)36 b(and)e(theoretical)i (computer)f(science")h([60)q(].)69 b(That)34 b(is)h(an)f(understatemen) m(t.)88 b(Not)35 b(only)f(is)h FC(P)0 4411 y FD(vs.)k FC(NP)g FD(the)g(de\014ning)f(question)h(of)g(our)f(\014eld;)43 b(it's)c(one)g(of)g(the)g(deep)s(est)g(questions)g(ev)m(er)g(ask)m(ed)h (for)e(whic)m(h)0 4524 y(w)m(e'd)30 b(kno)m(w)f(ho)m(w)g(to)h (recognize)i(an)d(answ)m(er.)1558 4491 y Fy(2)1667 4524 y FD(\(In)g(other)g(w)m(ords,)h(one)f(of)h(the)f(deep)s(est)g (questions)h(in)f FC(NP)p FD(.\))70 b(If)0 4637 y(y)m(ou)29 b(doubt)f(this,)h(read)g(the)g(Cla)m(y)g(Math)g(Institute's)g(list)h (of)e(million-dollar)j(prize)d(problems)g([12)q(],)i(and)e(notice)0 4750 y(ho)m(w)38 b FC(P)g FD(vs.)g FC(NP)g FD(stands)g(out,)i(not)e (merely)g(as)h(the)f(only)g(problem)f(of)h(the)g(sev)m(en)h(relev)-5 b(an)m(t)39 b(practically)-8 b(,)43 b(but)p 0 4829 1560 4 v 104 4883 a Fu(1)138 4915 y Ft(Supp)r(orted)30 b(b)n(y)g(an)g(NSF)h (Graduate)g(F)-6 b(ello)n(wship,)33 b(b)n(y)d(NSF)g(ITR)h(Gran)n(t)f (CCR-0121555,)36 b(and)30 b(b)n(y)g(the)g(Defense)h(Adv)l(anced)0 5006 y(Researc)n(h)26 b(Pro)t(jects)h(Agency)e(\(D)n(ARP)-6 b(A\).)104 5065 y Fu(2)138 5097 y Ft(W)g(e)19 b(are)h(taking)f Fs(P)g Ft(vs.)g Fs(NP)h Ft(here)f(as)h(represen)n(tativ)n(e)f(of)h(a)g (whole)g(constellation)h(of)f(related)f(questions,)i(whic)n(h)e(are)h (arguably)g(just)0 5188 y(as)28 b(imp)r(ortan)n(t:)38 b Fs(NP)28 b Ft(vs.)g Fs(P)p Fr(=)p Fs(p)r(oly)r Ft(,)g Fs(P)g Ft(vs.)f Fs(PSP)-6 b(A)n(CE)p Ft(,)28 b Fs(NP)g Ft(vs.)f Fs(coNP)q Ft(,)i Fs(BPP)e Ft(vs.)h Fs(BQP)p Ft(,)g(the)f(existence)h(of)g(public-k)n(ey)e(cryptograph)n(y)-6 b(,)0 5280 y(and)25 b(so)i(on.)60 b(F)-6 b(or)25 b(simplicit)n(y)-6 b(,)27 b(ho)n(w)n(ev)n(er,)f(w)n(e)g(fo)r(cus)g(on)g Fs(P)g Ft(vs.)g Fs(NP)p Ft(.)p eop end %%Page: 2 2 TeXDict begin 2 1 bop 0 91 a FD(as)38 b(the)g(only)g(one)g(pregnan)m(t) h(philosophically)-8 b(.)102 b(Do)s(es)39 b(the)f(abilit)m(y)h(to)g (recognize)g(an)f(answ)m(er)g(to)h(the)f(other)0 204 y(six)c(questions|or)h(to)g FC(P)f FD(vs.)g FC(NP)q FD(,)h(or)g(to)g (an)m(y)g(question|en)m(tail)h(the)e(abilit)m(y)i(to)f Fq(\014nd)44 b FD(an)35 b(answ)m(er?)86 b(W)-8 b(e)36 b(are)0 317 y(after)j(not)f(pro)5 b(jectiv)m(e)40 b(algebraic)g(v)-5 b(arieties)39 b(or)f(zeros)h(of)f(the)h(Riemann)e(zeta)j(function,)g (but)e(the)g(nature)g(of)0 430 y(mathematical)33 b(though)m(t)e (itself.)141 543 y(And)j(therein)h(lies)h(the)f(sub)5 b(ject)35 b(of)g(this)g(surv)m(ey)-8 b(.)90 b(If)35 b FC(P)g FD(vs.)g FC(NP)g FD(asks)g(something)h(so)f(ineluctably)h(meta-) 0 656 y(mathematical,)f(then)e(should)e(w)m(e)i(b)s(e)g(surprised)d(if) j(the)g(to)s(ols)g(of)g(mathematics)h(don't)f(su\016ce)f(to)i(answ)m (er)e(it?)0 769 y(In)h(other)i(w)m(ords,)g(could)f FC(P)g FD(vs.)g FC(NP)h FD(b)s(e)f(indep)s(enden)m(t)e(of)j(the)f(standard)g (axiom)h(systems,)g(suc)m(h)f(as)g(Zermelo-)0 882 y(F)-8 b(raenk)m(el)38 b(set)f(theory?)96 b(Whether)36 b(one)h(judges)f(this)g (plausible)h(seems)f(related)i(to)f(one's)g(view)f(on)h(another)0 995 y(question:)k(is)30 b FC(P)h FD(vs.)f FC(NP)h FD(\\really")h(a)f (question)f(ab)s(out)h(logic,)h(or)e(ab)s(out)g(com)m(binatorics?)141 1108 y(A)m(ttitudes)38 b(to)m(w)m(ard)f(the)f(last)h(question)g(ha)m(v) m(e)g(shifted)f(o)m(v)m(er)h(the)g(past)f(\014ft)m(y)g(y)m(ears.)95 b(In)36 b(G\177)-45 b(odel's)37 b(famous)0 1220 y(1956)30 b(letter)g(to)g(v)m(on)f(Neumann)e(\(translated)j(in)e([60)r(]\),)h (where)f FC(P)h FD(vs.)g FC(NP)g FD(w)m(as)g(\014rst)f(p)s(osed,)g (G\177)-45 b(odel)30 b(apparen)m(tly)0 1333 y(sa)m(w)h(the)f(problem)g (as)h(a)f(\014nitary)g(analogue)i(of)f(the)f(Hilb)s(ert)h(En)m(tsc)m (heidungsproblem:)3063 1300 y Fy(3)227 1546 y FD(It)38 b(is)f(eviden)m(t)h(that)g(one)f(can)g(easily)i(construct)e(a)h(T)-8 b(uring)36 b(mac)m(hine)i(whic)m(h,)h(for)e(eac)m(h)h(form)m(ula)227 1659 y Fp(F)50 b FD(of)37 b(the)g(predicate)h(calculus)f(and)f(for)h (ev)m(ery)h(natural)e(n)m(um)m(b)s(er)g Fp(n)p FD(,)i(will)f(allo)m(w)i (one)e(to)g(decide)227 1772 y(if)g Fp(F)50 b FD(has)36 b(a)h(pro)s(of)f(of)h(length)g Fp(n)p FD(.)95 b(Let)37 b(\011)15 b(\()q Fp(F)s(;)g(n)p FD(\))36 b(b)s(e)g(the)h(n)m(um)m(b)s (er)f(of)g(steps)h(that)g(the)g(mac)m(hine)227 1885 y(requires)c(for)g (that)h(and)e(let)j Fp(')15 b FD(\()q Fp(n)p FD(\))29 b(=)h(max)1727 1899 y Fo(F)1801 1885 y FD(\011)15 b(\()p Fp(F)s(;)g(n)p FD(\))q(.)82 b(The)33 b(question)g(is,)h(ho)m(w)f(fast)h (do)s(es)f Fp(')15 b FD(\()q Fp(n)p FD(\))227 1998 y(gro)m(w)32 b(for)f(an)g(optimal)i(mac)m(hine.)75 b(One)31 b(can)g(sho)m(w)g(that)h Fp(')15 b FD(\()q Fp(n)p FD(\))27 b Fn(\025)f Fp(K)7 b(n)p FD(.)74 b(If)31 b(there)g(actually)i(w)m(ere)227 2110 y(a)f(mac)m(hine)h(with)e Fp(')15 b FD(\()q Fp(n)p FD(\))27 b Fn(\030)g Fp(K)7 b(n)31 b FD(\(or)h(ev)m(en)g(only)g(with)f Fn(\030)c Fp(K)7 b(n)2367 2077 y Fy(2)2406 2110 y FD(\),)32 b(this)g(w)m(ould)f(ha)m(v)m(e)i(consequences)227 2223 y(of)i(the)g(greatest)h(magnitude.)88 b(That)35 b(is)g(to)g(sa)m(y)-8 b(,)37 b(it)e(w)m(ould)g(clearly)g(indicate)h(that,)h(despite)d(the)227 2336 y(unsolv)-5 b(abilit)m(y)37 b(of)e(the)h(En)m(tsc)m (heidungsproblem,)g(the)f(men)m(tal)i(e\013ort)f(of)f(the)h (mathematician)h(in)227 2449 y(the)21 b(case)h(of)g(y)m(es-or-no)g (questions)f(could)g(b)s(e)f(completely)j(\(fo)s(otnote:)37 b(apart)22 b(from)e(the)h(p)s(ostulation)227 2562 y(of)27 b(axioms\))g(replaced)g(b)m(y)f(mac)m(hines.)66 b(One)26 b(w)m(ould)g(indeed)g(ha)m(v)m(e)i(to)f(simply)f(select)i(an)e Fp(n)g FD(so)h(large)227 2675 y(that,)g(if)f(the)f(mac)m(hine)h(yields) f(no)g(result,)i(there)e(w)m(ould)g(then)g(also)h(b)s(e)f(no)g(reason)g (to)h(think)f(further)227 2788 y(ab)s(out)30 b(the)h(problem.)141 3000 y(In)20 b(the)g(sev)m(en)m(ties,)25 b(when)19 b(serious)h(w)m(ork) g(on)h FC(P)f FD(vs.)g FC(NP)h FD(b)s(egan)f(follo)m(wing)i(the)e (disco)m(v)m(ery)i(of)e FC(NP)q FD(-completeness)0 3113 y(b)m(y)32 b(Co)s(ok)h([14)q(],)h(Karp)d([30)q(],)j(and)e(Levin)g([36)q (],)i(the)f(problem)f(con)m(tin)m(ued)h(to)g(b)s(e)f(seen)h(in)f (logical)j(terms.)79 b(P)m(eo-)0 3226 y(ple)35 b(tried)g(to)h(separate) g FC(P)g FD(and)e FC(NP)i FD(using)e(the)i(same)f(ideas)h(that)f(w)m (ork)m(ed)h(in)f(recursion)g(theory;)j(this)d(is)g(the)0 3339 y(con)m(text)d(of)e(the)g(Bak)m(er-Gill-Solo)m(v)-5 b(a)m(y)35 b([4)q(])30 b(result)g(that)g FC(P)g FD(vs.)g FC(NP)h FD(admits)f(con)m(tradictory)h(relativizations.)74 b(In)0 3452 y(Section)27 b(3)h(w)m(e'll)f(see)h(other)f(logic-orien)m (ted)i(w)m(ork)e(from)f(this)h(p)s(erio)s(d,)f(whic)m(h)h(explicitly)h (raised)f(the)f(p)s(ossibilit)m(y)0 3565 y(that)38 b FC(P)f Fn(6)p FD(=)g FC(NP)g FD(migh)m(t)h(go)h(the)e(w)m(a)m(y)h(of)g (the)g(Con)m(tin)m(uum)e(Hyp)s(othesis|its)i(truth)e(forev)m(er)i (unkno)m(w)m(able,)i(or)0 3678 y(dep)s(enden)m(t)29 b(up)s(on)g(whic)m (h)h(axioms)h(w)m(e)g(c)m(ho)s(ose.)141 3791 y(In)22 b(the)h(eigh)m(ties,)j(the)d(com)m(binatorial)h(view)f(b)s(ecame)g (dominan)m(t,)i(in)d(the)h(w)m(ak)m(e)h(of)e(the)h(circuit)g(lo)m(w)m (er)h(b)s(ounds)0 3904 y(of)k(F)-8 b(urst-Saxe-Sipser)28 b([18)q(],)h(Ajtai)g([2)q(],)g(Razb)s(oro)m(v)g([50)q(,)f(52)q(],)h (and)e(Smolensky)h([61)q(].)68 b(On)28 b(this)f(view,)i FC(P)f FD(vs.)h FC(NP)0 4017 y FD(is)c(no)g(more)h(lik)m(ely)g(to)g(b)s (e)f(formally)g(indep)s(enden)m(t)f(than)h(Goldbac)m(h's)h(Conjecture,) h(the)e(Riemann)g(Hyp)s(othesis,)0 4130 y(or)h(an)m(y)g(other)g (`natural')h(mathematical)h(problem.)65 b(Pro)m(ving)26 b FC(P)f Fn(6)p FD(=)g FC(NP)i FD(\(and)e(indeed)h(the)g(stronger)g (statemen)m(t)0 4242 y FC(NP)j Fm(*)g FC(P)p Fp(=)p FC(p)s(oly)q FD(\))k(is)g(really)g(just)f(a)h(matter)h(of)e(rolling)i(up)d(our)h (sleev)m(es)i(and)e(analyzing)i(increasingly)f(p)s(o)m(w)m(erful)0 4355 y(kinds)c(of)i(circuits.)141 4468 y(The)23 b(nineties)h(sa)m(w)g (a)g(return)f(to)h(the)g(logicism)h(and)e(bro)s(o)s(ding)f(p)s (essimism)h(of)h(the)f(sev)m(en)m(ties.)64 b(As)24 b(discussed)0 4581 y(in)34 b(Section)h(4,)h(Razb)s(oro)m(v)f(and)e(Rudic)m(h)h([56)q (])h(p)s(oin)m(ted)f(out)g(a)h(basic)g(limitation)h(of)e(the)h(circuit) g(lo)m(w)m(er)g(b)s(ound)0 4694 y(tec)m(hniques)h(from)f(the)h(eigh)m (ties:)52 b(these)36 b(tec)m(hniques)g(w)m(ould)g(\(almost\))h(argue)f (against)g(themselv)m(es,)i(yielding)p 0 4778 1560 4 v 104 4832 a Fu(3)138 4864 y Ft(The)31 b(En)n(tsc)n(heidungsproblem)f (asks)h(for)h(a)e(pro)r(cedure)h(that,)h(giv)n(en)e(a)h(mathematical)h (statemen)n(t,)g(either)f(\014nds)e(a)i(pro)r(of)h(or)0 4955 y(tells)27 b(us)f(that)f(none)h(exists.)61 b Fs(P)22 b Ft(=)f Fs(NP)26 b Ft(asks)h(for)f(an)g Fl(e\016cient)34 b Ft(pro)r(cedure)26 b(that)f(\014nds)g(a)h Fl(short)35 b Ft(pro)r(of.)62 b(In)25 b(one)h(sense,)h(ho)n(w)n(ev)n(er,)f Fs(P)0 5046 y Ft(vs.)i Fs(NP)g Ft(is)g Fl(not)36 b Ft(a)28 b(\014nitary)f(analogue)i(of)g(the)e(En)n(tsc)n(heidungsproblem.)68 b(F)-6 b(or)28 b(once)g(w)n(e)g(require)g(all)h(branc)n(hes)e(of)i(a)f (computation)0 5138 y(to)c(halt)h(ev)n(en)n(tually)-6 b(,)24 b(the)f(`nondeterministically)j(recursiv)n(e')f(languages)h(are) f(just)f(the)g(recursiv)n(e)g(languages)i(themselv)n(es,)f(not)f(the)0 5229 y(recursiv)n(ely)f(en)n(umerable)f(languages.)58 b(So)22 b(the)h(distinction)g(b)r(et)n(w)n(een)f(\014nding)g(and)g(v)n (erifying)h(a)g(b)r(ounded-size)f(ob)t(ject)h(is)g(one)g(that)0 5320 y(do)r(esn't)j(exist)g(in)f(the)h(recursion-theory)f(w)n(orld.)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 0 91 a FD(e\016cien)m(t)35 b(w)m(a)m(ys)g(to)f (solv)m(e)h(the)f(v)m(ery)g(problems)f(they)h(w)m(ere)h(supp)s(osed)c (to)k(pro)m(v)m(e)f(in)m(tractable!)70 b(Subsequen)m(tly)-8 b(,)0 204 y(as)27 b(w)m(e'll)h(see)g(in)e(Section)i(4.1,)h(Razb)s(oro)m (v)f([55)q(])f(used)f(this)h(idea)g(to)h(pro)m(v)m(e,)h(under)c (cryptographic)i(assumptions,)0 317 y(that)k FC(P)f FD(vs.)h FC(NP)g FD(is)f(indep)s(enden)m(t)f(of)i(certain)g(theories)g(of)g(`b)s (ounded)d(arithmetic.')141 430 y(I)22 b(don't)g(kno)m(w)f(if)h(it's)h (p)s(ossible)e(an)m(y)h(longer)h(to)f(discern)g(a)g(unifying)f(trend.) 59 b(Mulm)m(uley)22 b(and)f(Sohoni)h([39)q(,)g(57)q(])0 543 y(ha)m(v)m(e)34 b(prop)s(osed)d(to)i(tac)m(kle)i FC(P)d FD(vs.)h FC(NP)g FD(using)e(algebraic)k(geometry|an)e(approac)m (h)g(that,)h(they)e(think,)h(migh)m(t)0 656 y(escap)s(e)f(the)f(ja)m (ws)g(of)h(Razb)s(oro)m(v)f(and)g(Rudic)m(h.)74 b(Using)31 b(the)g(deep)g(result)g(that)h FC(MIP)25 b FD(=)g FC(NEXP)32 b FD([3],)g(Buhrman,)0 769 y(F)-8 b(ortno)m(w,)30 b(and)e(Thierauf)f ([8)q(])h(sho)m(w)m(ed)h(that)f FC(MA)1696 784 y Fk(EXP)1834 769 y FD(,)h(the)f(exp)s(onen)m(tial-time)j(analogue)e(of)g FC(MA)o FD(,)g(do)s(esn't)f(ha)m(v)m(e)0 882 y(p)s(olynomial-size)33 b(circuits.)74 b(This)30 b(result)h(is)g(notable)h(b)s(ecause)f(it)h(a) m(v)m(oids)g(b)s(oth)e(the)i(Bak)m(er-Gill-Solo)m(v)-5 b(a)m(y)36 b(and)0 995 y(the)31 b(Razb)s(oro)m(v-Rudic)m(h)g (limitations.)72 b(So)30 b(p)s(erhaps)f(there's)i(hop)s(e)f(after)g (all.)141 1108 y(In)22 b(an)m(y)i(ev)m(en)m(t,)i(ho)m(w)m(ev)m(er,)g (it)e(seems)f(lik)m(ely)h(that)g(future)e(w)m(ork)h(on)g FC(P)g FD(vs.)g FC(NP)g FD(will)h(b)s(e)e(inseparable)h(from)g(w)m(ork) 0 1220 y(on)33 b(the)h Fq(lo)-5 b(gic)g(al)37 b(status)42 b FD(of)34 b(the)f(question.)84 b(Again)35 b(and)d(again)j(in)e(this)h (surv)m(ey)-8 b(,)34 b(w)m(e'll)h(encoun)m(ter)f(the)g(bizarre)0 1333 y(self-referen)m(tial)g(nature)e(of)g FC(P)d Fn(6)p FD(=)f FC(NP)p FD(|a)33 b(conjecture)g(that)f(all)h(but)f(asserts)g (the)h(titanic)g(di\016cult)m(y)g(of)f(\014nding)0 1446 y(its)d(o)m(wn)h(pro)s(of.)68 b(F)-8 b(or)30 b(this)f(reason,)h(I)f (think)f(that)i(an)m(y)m(one)g(in)m(terested)h(in)d(complexit)m(y|ev)m (en)k(those)d(who,)h(lik)m(e)0 1559 y(me,)38 b(ha)m(v)m(e)f(no)e(logic) j(bac)m(kground)e(whatso)s(ev)m(er|ough)m(t)h(to)f(learn)g(something)h (ab)s(out)e(what)h(it)g(w)m(ould)g(mean)0 1672 y(for)h FC(P)g FD(vs.)g FC(NP)h FD(to)g(b)s(e)e(formally)i(indep)s(enden)m(t,)g (and)f(what)g(can)g(b)s(e)g(said)g(for)g(and)g(against)h(that)g(p)s (ossibilit)m(y)-8 b(.)0 1785 y(Hence)28 b(this)g(surv)m(ey)-8 b(.)67 b(Although)28 b(it)g(do)s(es)g(con)m(tain)g(the)g(recommended)f (daily)h(allo)m(w)m(ance)j(of)c(theorems)h(\(for)g(an)0 1898 y(a)m(v)m(erage-w)m(eigh)m(t)35 b(theoretician\),)e(its)e(cen)m (tral)g(concern)g(is)f(philosophical:)227 2078 y Fq(How)39 b(c)-5 b(ould)40 b(such)f(a)g(cle)-5 b(ar)39 b(mathematic)-5 b(al)42 b(question|a)d(question)g(ab)-5 b(out)39 b(\014nite)g(machines) h(and)227 2191 y(pr)-5 b(oblems,)30 b(a)c(question)h(of)g(gr)-5 b(e)g(at)27 b(imp)-5 b(ortanc)g(e)29 b(for)e(scienc)-5 b(e)26 b(and)i(industry|b)-5 b(e)27 b(for)-5 b(ever)27 b(unanswer-)227 2304 y(able?)141 2485 y FD(Th)m(us)38 b(I'll)h(start,)j(as)e(I'll)f(end,)i(b)m(y)e(talking)h(not)f(ab)s(out)g FC(P)g FD(vs.)g FC(NP)p FD(,)i(but)e(ab)s(out)f(logic,)43 b(pro)m(v)-5 b(abilit)m(y)d(,)44 b(and)0 2597 y(truth.)0 2879 y FE(2)135 b(Logic)45 b(Primer)0 3082 y FD(Ha)m(v)m(e)26 b(y)m(ou)e(ev)m(er)h(la)m(y)g(a)m(w)m(ak)m(e)i(at)e(nigh)m(t,)h (terri\014ed)d(of)i(what)f(w)m(ould)f(happ)s(en)g(w)m(ere)h(the)h (Zermelo-F)-8 b(raenk)m(el)26 b(axioms)0 3195 y(found)36 b(to)j(b)s(e)e(inconsisten)m(t)i(the)f(next)f(morning?)100 b(W)-8 b(ould)38 b(bridges)f(collapse?)102 b(W)-8 b(ould)38 b(ev)m(ery)h(pap)s(er)d(ev)m(er)0 3308 y(published)c(in)i(STOC)e(and)h (F)m(OCS)h(ha)m(v)m(e)h(to)f(b)s(e)g(withdra)m(wn?)83 b(\(\\The)34 b(theorems)g(are)h(still)f(true,)h(but)e(so)i(are)0 3421 y(their)h(negations."\))73 b(Merely)37 b(con)m(templating)h(suc)m (h)d(p)s(ossibilities)h(is)g(enough)g(to)g(cause)g(feelings)h(of)f(v)m (ertigo.)0 3533 y(Ho)m(w)f(could)f(a)h(theorem)f(b)s(e)g(in)m(v)-5 b(alidated)35 b(b)s(ecause)g(of)f(axioms)h(that)g(seem)f(to)h(ha)m(v)m (e)g(nothing)g(to)f(do)h(with)e(it?)0 3646 y(It)28 b(w)m(ould)f(b)s(e)g (as)g(if)h(y)m(ou)f(added)g(up)f(a)i(restauran)m(t)g(bill,)h(and)e (then)g(a)g(ph)m(ysicist)h(explained)g(that)g(y)m(our)f(total)j(w)m(as) 0 3759 y(wrong)g(b)s(ecause)g(of)h(the)f(expansion)h(of)f(the)h(univ)m (erse.)141 3872 y(This)41 b(is)h(the)f(sort)h(of)g(issue)f (philosophers)g(lik)m(e)i(Wittgenstein)h(talk)m(ed)f(ab)s(out)e(a)h (lot.)117 b(I)41 b(w)m(on't)i(try)e(to)0 3985 y(summarize)h(what)g (they)g(said,)k(for)c(the)g(same)g(reason)h(that)g(T)-8 b(uring,)44 b(after)f(sitting)g(in)f(on)g(Wittgenstein's)0 4098 y(seminar,)27 b(b)s(ecame)g(exasp)s(erated)f(and)g(dropp)s(ed)e (out)j([38)q(].)65 b(My)27 b(concern)f(is)h(more)f(practical:)40 b(should)26 b(w)m(e,)h(who)0 4211 y(dw)m(ell)k(in)f(the)g(to)m(w)m(er)i (of)f(mathematics,)h(w)m(orry)e(ab)s(out)g(a)h(collapse)h(of)e(the)h (foundations?)141 4324 y(In)j(m)m(y)g(opinion,)h(no.)87 b(If)34 b(y)m(ou)g(don't)h(b)s(eliev)m(e)g(Euclid's)f(pro)s(of)g(that)h (there)f(are)h(in\014nitely)f(man)m(y)g(primes,)0 4437 y(then)39 b(I)g(don't)h(kno)m(w)f(wh)m(y)g(seeing)h(a)g(formal)g(pro)s (of)f(in)g(ZF)g(set)h(theory)g(should)e(quell)i(y)m(our)f(doubts.)106 b(Y)-8 b(ou)0 4550 y(could)34 b(den)m(y)g(Mo)s(dus)f(P)m(onens,)j(y)m (ou)e(could)g(demand)g(a)g(formal)g(pro)s(of)g(for)g(the)g(assertion)h (\\The)f(in\014nitude)f(of)0 4663 y(primes)d(is)h(a)g(theorem)g(of)f (ZF")h(itself)h(\(ad)e(in\014nitum\),)g(y)m(ou)h(could)g(refuse)f(to)h (iden)m(tify)g(the)g(formal)g(notions)g(of)0 4775 y(`prime')f(or)g (`in\014nit)m(y')g(with)f(the)h(informal)g(ones,)h(and)e(so)h(on.)70 b(Therefore)30 b Fq(the)i(informal)i(pr)-5 b(o)g(of)35 b(alr)-5 b(e)g(ady)34 b(yields)0 4888 y(as)29 b(much)f(c)-5 b(ertainty)29 b(ab)-5 b(out)30 b(the)e(in\014nitude)g(of)h(primes)g(as) g(it's)f(humanly)h(p)-5 b(ossible)30 b(to)e(have)p FD(.)65 b(If)25 b(w)m(e)h(try)g(to)g(place)0 5001 y(the)33 b(pro)s(of)f(on)g(a) h(\\more)g(secure)g(foundation,")g(then)f(the)h(foundation)g(is)f(as)h (op)s(en)f(to)h(doubt)f(as)h(the)g(p)s(ositiv)m(e)0 5114 y(in)m(tegers)f(are.)141 5227 y(If)h(y)m(ou)h(accept)g(this,)h(I)e (think)f(it)i(b)s(ecomes)g(easier)g(to)g(understand)d(what)j(a)f (formal)h(system)f(is.)83 b(It's)34 b(just)0 5340 y(a)g(w)m(a)m(y)g(to) g(co)s(dify)f(a)h(form)f(of)g(reasoning|whic)m(h)g(presumably)g(w)m (e'v)m(e)h(already)g(accepted)h(as)e(v)-5 b(alid|so)34 b(that)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 0 91 a FD(\(1\))34 b(w)m(e)g(can)f(program)g(a)h (computer)f(to)h(reason)f(for)g(us,)h(and)e(\(2\))j(w)m(e)e(can)h (explore)f(the)h(ultimate)g(limitations)0 204 y(of)d(that)g(form)e(of)i (reasoning.)0 448 y Fj(2.1)112 b(The)38 b(First-Order)g(Sen)m(tences)g (Game)0 619 y FD(As)31 b(an)g(example,)i(consider)e(the)h(de\014nition) f(of)g(a)h(group.)74 b(W)-8 b(e)33 b(ha)m(v)m(e)f(a)g(ternary)f (predicate)h Fp(M)25 b FD(\()q Fp(x;)15 b(y)s(;)g(z)t FD(\))32 b(\(in)m(tu-)0 732 y(itiv)m(ely)g Fp(x)20 b Fn(\001)h Fp(y)28 b FD(=)d Fp(z)t FD(\))31 b(that)g(satis\014es)g(a)f (set)h(of)g(three)f(axioms,)i(called)f(a)g Fq(the)-5 b(ory)8 b FD(:)66 945 y(\(1\))46 b Fi(Uniqueness.)72 b Fn(8)p Fp(x;)15 b(y)33 b Fn(9)p Fp(z)49 b FD(\()q Fp(M)25 b FD(\()p Fp(x;)15 b(y)s(;)g(z)t FD(\))22 b Fn(^)e(8)p Fp(w)47 b FD(\()p Fp(M)26 b FD(\()p Fp(x;)15 b(y)s(;)g(w)r FD(\))27 b(=)-15 b Fn(\))25 b FD(\()p Fp(w)j FD(=)d Fp(z)t FD(\)\))q(\))66 1132 y(\(2\))46 b Fi(Asso)s(ciativit)m(y)-9 b(.)72 b Fn(8)p Fp(x;)15 b(y)s(;)g(z)t(;)g(w)49 b FD(\()p Fn(9)p Fp(v)33 b(M)26 b FD(\()p Fp(x;)15 b(y)s(;)g(v)s FD(\))22 b Fn(^)d Fp(M)26 b FD(\()p Fp(v)s(;)15 b(z)t(;)g(w)r FD(\))r(\))26 b(=)-15 b Fn(\))25 b FD(\()p Fn(9)p Fp(v)33 b(M)25 b FD(\()q Fp(y)s(;)15 b(z)t(;)g(v)s FD(\))21 b Fn(^)f Fp(M)26 b FD(\()p Fp(x;)15 b(v)s(;)g(w)r FD(\))r(\))66 1320 y(\(3\))46 b Fi(Iden)m(tit)m(y)35 b(and)f(In)m(v)m(erse.)71 b Fn(9)p Fp(x)30 b Fn(8)p Fp(y)48 b FD(\()p Fp(M)26 b FD(\()p Fp(x;)15 b(y)s(;)g(y)s FD(\))21 b Fn(^)f Fp(M)25 b FD(\()p Fp(y)s(;)15 b(x;)g(y)s FD(\))21 b Fn(^)f(9)p Fp(z)49 b FD(\()q Fp(M)25 b FD(\()p Fp(y)s(;)15 b(z)t(;)g(x)p FD(\))22 b Fn(^)e Fp(M)25 b FD(\()p Fp(z)t(;)15 b(y)s(;)g(x)p FD(\))q(\))q(\))141 1533 y(Then)37 b(a)h Fq(mo)-5 b(del)49 b FD(for)37 b(the)h(theory)g(is)g(just)f(a)h(set)g Fp(U)48 b FD(of)38 b(ob)5 b(jects)38 b(\(called)i(a)e Fq(universe)7 b FD(\),)39 b(together)h(with)d(an)0 1645 y(assignmen)m(t)32 b(of)g(`true')g(or)g(`false')h(to)f Fp(M)26 b FD(\()p Fp(x;)15 b(y)s(;)g(z)t FD(\))33 b(for)e(ev)m(ery)i Fp(x;)15 b(y)s(;)g(z)36 b FD(in)c Fp(U)10 b FD(,)32 b(suc)m(h)f(that)h(the)g (axioms)h(hold)e(when)0 1758 y(the)f(quan)m(ti\014ers)h(range)f(o)m(v)m (er)i Fp(U)10 b FD(.)71 b(In)29 b(general,)j(an)e(axiom)h(can)g(b)s(e)e (an)m(y)i(\014rst-order)f(sen)m(tence|meaning)h(that)0 1871 y(it)39 b(can)g(ha)m(v)m(e)g(v)-5 b(ariable,)42 b(constan)m(t,)g(and)37 b(predicate)j(sym)m(b)s(ols;)i(Bo)s(olean)e (connectiv)m(es)g(\()p Fn(^)p FD(,)h Fn(_)p FD(,)f Fh(q)p FD(,)h(=)-15 b Fn(\))p FD(,)40 b(etc.\);)0 1984 y(quan)m(ti\014ers)d (\()p Fn(8)p FD(,)i Fn(9)p FD(\);)h(and)d(equal)g(signs)g(\(=\).)99 b(The)36 b(equal)i(sign)f(is)g(not)h(shorthand)d(for)i(a)h(binary)e (predicate)0 2097 y Fp(E)20 b FD(\()q Fp(x;)15 b(y)s FD(\);)35 b(it)f(really)g(means)e(that)i(t)m(w)m(o)h(ob)5 b(jects)33 b(are)h(the)f(same.)82 b(Crucially)-8 b(,)35 b(the)e(quan)m(ti\014ers)g(can)g(range)h(only)0 2210 y(o)m(v)m(er)e(ob)5 b(jects)31 b(in)f Fp(U)10 b FD(,)30 b(not)h Fq(sets)38 b FD(of)31 b(ob)5 b(jects.)71 b(That's)31 b(what)f(`\014rst-order')g(means.)141 2323 y(Ho)m(w)23 b(m)m(uc)m(h)f(can)h(w)m(e)g(sa)m(y)g(using)f(these)g(\014rst-order)g (sen)m(tences?)61 b(T)-8 b(o)23 b(get)g(some)g(in)m(tuition,)i(let's)e (ask)g(ho)m(w)f(w)m(ell)0 2436 y(w)m(e)29 b(can)h(con)m(trol)g(the)f Fq(c)-5 b(ar)g(dinality)40 b FD(of)29 b(the)g(univ)m(erse)g Fp(U)10 b FD(.)69 b(Groups)28 b(can)h(b)s(e)f(\014nite,)i(coun)m (table,)h(or)d(uncoun)m(table,)0 2549 y(so)34 b(of)g(course)g(the)f (axioms)i(for)e(a)h(group)f(ha)m(v)m(e)i(\014nite,)g(coun)m(table,)h (and)d(uncoun)m(table)h(mo)s(dels.)84 b(If)33 b(w)m(e)h(w)m(an)m(t,)0 2662 y(though,)c(w)m(e)h(can)g(force)g Fn(j)p Fp(U)10 b Fn(j)31 b FD(to)g(b)s(e)e(at)j(most)e(3:)136 2874 y Fn(\017)46 b(9)p Fp(x;)15 b(y)s(;)g(z)35 b Fn(8)p Fp(w)47 b FD(\()q Fp(w)28 b FD(=)d Fp(x)20 b Fn(_)g Fp(w)27 b FD(=)e Fp(y)e Fn(_)d Fp(w)28 b FD(=)d Fp(z)t FD(\))141 3087 y(W)-8 b(e)34 b(can)g(also)g(force)f Fn(j)p Fp(U)10 b Fn(j)34 b FD(to)f(b)s(e)g(in\014nite.)81 b(P)m(eano)34 b(Arithmetic)g(uses)f(a)g(binary)f(predicate)i Fp(S)20 b FD(\()q Fp(x;)15 b(y)s FD(\))33 b(\(in)m(tu-)0 3200 y(itiv)m(ely)f Fp(y)c FD(=)d Fp(x)20 b FD(+)g(1\))31 b(that)g(satis\014es)g(these)g(t)m(w)m(o)h(axioms:)66 3412 y(\(1\))46 b Fi(Zero.)71 b Fn(9)p Fp(y)33 b Fn(8)p Fp(x)d Fh(q)p Fp(S)20 b FD(\()q Fp(x;)15 b(y)s FD(\))66 3600 y(\(2\))46 b Fi(Unique)36 b(Successor.)72 b Fn(8)p Fp(x)30 b Fn(9)p Fp(y)48 b FD(\()p Fp(S)20 b FD(\()q Fp(x;)15 b(y)s FD(\))g Fn(^)p Fh(q)g FD(\()q Fp(y)28 b FD(=)d Fp(x)p FD(\))c Fn(^)e(8)p Fp(z)50 b FD(\()p Fp(S)20 b FD(\()q Fp(x;)15 b(z)t FD(\))26 b(=)-15 b Fn(\))24 b FD(\()q Fp(z)29 b FD(=)c Fp(y)s FD(\)\))q(\))141 3812 y(Can)i(w)m(e)h(force)g Fn(j)p Fp(U)10 b Fn(j)27 b FD(to)h(b)s(e)f (uncoun)m(table?)67 b(W)-8 b(e)28 b(migh)m(t)g(try)g(to)g(b)m(y)f (writing)g(do)m(wn)g(axioms)h(that)g(encompass)0 3925 y(all)37 b(of)f(mathematics.)94 b(That)35 b(sounds)g(lik)m(e)i(a)f (tall)h(order,)g(but)e(as)h(is)g(w)m(ell)g(kno)m(wn,)h(it's)g(enough)e (to)i(describ)s(e)0 4038 y(a)d(univ)m(erse)g(whose)f(ob)5 b(jects)34 b(are)g Fq(sets)p FD(.)1348 4005 y Fy(4)1472 4038 y FD(What)g(do)g(these)g(sets)g(con)m(tain?)85 b(Other)33 b(sets!)84 b(Zermelo-F)-8 b(raenk)m(el)0 4151 y(\(ZF\))33 b(set)f(theory)h(in)m(v)m(olv)m(es)h(a)e(binary)g(predicate)h Fp(S)20 b FD(\()p Fp(x;)15 b(y)s FD(\))33 b(\(in)m(tuitiv)m(ely)h Fp(x)28 b Fn(2)g Fp(y)s FD(\),)33 b(that)g(satis\014es)f(the)g(follo)m (wing)0 4264 y(axioms.)73 b(\(I'll)32 b(write)f(the)g(axioms)h(in)e (English,)h(since)g(it)g(should)f(b)s(e)g(ob)m(vious)i(b)m(y)e(no)m(w)h (ho)m(w)g(to)h(con)m(v)m(ert)g(them)0 4377 y(to)f(\014rst-order)f (notation.\))66 4589 y(\(1\))46 b Fi(Empt)m(y)35 b(Set.)70 b FD(There)30 b(exists)h(a)g(set)g(\(denoted)g Fm(?)p FD(\))f(that)h(do)s(es)f(not)h(con)m(tain)g(an)m(y)g(mem)m(b)s(ers.)66 4777 y(\(2\))46 b Fi(Extensionalit)m(y)-9 b(.)71 b FD(If)30 b(t)m(w)m(o)i(sets)f(con)m(tain)g(the)g(same)g(mem)m(b)s(ers)e(then)h (they)h(are)g(equal.)66 4965 y(\(3\))46 b Fi(P)m(airing.)72 b FD(F)-8 b(or)31 b(all)g(sets)g Fp(x)f FD(and)g Fp(y)j FD(there)e(exists)g(a)g(set)f(whose)h(mem)m(b)s(ers)e(are)i Fp(x)f FD(and)g Fp(y)s FD(.)p 0 5049 1560 4 v 104 5103 a Fu(4)138 5134 y Ft(Ho)n(w)f(can)g(w)n(e)g(use)f(axioms)i(to)f (de\014ne)f(sets,)i(if)f(w)n(e)g(need)f(the)h(concept)f(of)h(set)g(ev)n (en)f(to)h(sa)n(y)g(what)g(w)n(e)g(mean)f(b)n(y)g(a)h Fl(mo)l(del)36 b Ft(for)0 5226 y(axioms?)77 b(This)31 b(is)f(the)f(kind)g(of)i(parado)n(x)e(that)h(I)f(think)g(v)l(anishes)h (once)g(w)n(e)g(giv)n(e)g(up)f(the)g(idea)h(of)h(putting)e(mathematics) i(on)f(a)0 5317 y(`more)23 b(secure)f(foundation,')i(and)e(see)h (formal)g(systems)g(as)f(just)h(co)r(difying)g(forms)g(of)g(reasoning)g (w)n(e'v)n(e)f(already)h(accepted)f(as)h(v)l(alid.)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 66 91 a FD(\(4\))46 b Fi(Union.)72 b FD(F)-8 b(or)31 b(all)h(sets)f Fp(x)f FD(and)g Fp(y)j FD(there)e(exists)g(a)f(set)h(\(denoted)g Fp(x)20 b Fn([)g Fp(y)s FD(\))31 b(that)g(con)m(tains)h Fp(z)i FD(if)d(and)e(only)i(if) 227 204 y Fp(z)f Fn(2)25 b Fp(x)30 b FD(or)g Fp(z)g Fn(2)25 b Fp(y)s FD(.)66 392 y(\(5\))46 b Fi(In\014nit)m(y)-9 b(.)71 b FD(There)30 b(exists)h(a)g(set)g Fp(x)f FD(that)h(con)m(tains) h Fm(?)e FD(and)f(that)i(con)m(tains)h Fp(y)23 b Fn([)d(f)p Fp(y)s Fn(g)31 b FD(for)f(ev)m(ery)h Fp(y)d Fn(2)d Fp(x)p FD(.)66 579 y(\(6\))46 b Fi(P)m(o)m(w)m(er)30 b(Set.)64 b FD(F)-8 b(or)26 b(all)g(sets)g Fp(x)g FD(there)f(exists)i(a)e(set)h (\(denoted)g(2)2408 547 y Fo(x)2453 579 y FD(\))f(that)h(con)m(tains)h Fp(y)h FD(if)e(and)f(only)g(if)h Fp(y)i Fn(\022)d Fp(x)p FD(.)66 767 y(\(7\))46 b Fi(Replacemen)m(t)34 b(for)f(Predicate)g Fp(A)p Fi(.)69 b FD(F)-8 b(or)30 b(all)f(sets)g Fp(u)p FD(,)h(if)e(for)h(all)h Fp(x)25 b Fn(2)g Fp(u)j FD(there)h(exists)h(a)f (unique)f Fp(y)j FD(suc)m(h)227 880 y(that)39 b Fp(A)15 b FD(\()p Fp(x;)g(y)s FD(\))q(,)40 b(then)d(there)h(exists)g(a)h Fp(z)j FD(suc)m(h)37 b(that)h(for)g(all)g Fp(x)g Fn(2)f Fp(u)p FD(,)j(there)e(exists)g(a)g Fp(y)j Fn(2)c Fp(z)42 b FD(suc)m(h)37 b(that)227 993 y Fp(A)15 b FD(\()q Fp(x;)g(y)s FD(\))q(.)66 1181 y(\(8\))46 b Fi(F)-9 b(oundation.)81 b FD(All)33 b(nonempt)m(y)g(sets)g Fp(x)g FD(con)m(tain)h(a)f(mem)m(b)s (er)f Fp(y)k FD(suc)m(h)c(that)i(for)e(all)i Fp(z)t FD(,)g(either)f Fp(z)44 b(=)-56 b Fn(2)29 b Fp(x)k FD(or)227 1293 y Fp(z)40 b(=)-55 b Fn(2)25 b Fp(y)s FD(.)141 1506 y(There)33 b(are)h(actually)h (in\014nitely)e(man)m(y)h(axioms)g(ab)s(o)m(v)m(e,)i(since)d(w)m(e)h (ha)m(v)m(e)h(an)e(Axiom)h(of)g(Replacemen)m(t)h(for)0 1619 y(ev)m(ery)f(binary)f(predicate)h Fp(A)15 b FD(\()q Fp(x;)g(y)s FD(\).)83 b(This)32 b(do)s(esn't)i(cause)f(problems)g (\(though)g(if)h(w)m(e)f(don't)h(lik)m(e)g(it,)h(it)f(turns)0 1732 y(out)e(that)g(there's)g(an)g(equiv)-5 b(alen)m(t,)34 b(more)d(complicated)j(system)e(with)f(\014nitely)h(man)m(y)g(axioms,)h (called)g(G\177)-45 b(odel-)0 1845 y(Berna)m(ys)31 b(set)g(theory\).) 141 1958 y(So,)e(do)g(all)h(mo)s(dels)f(of)g(ZF)g(ha)m(v)m(e)h(uncoun)m (tably)f(man)m(y)g(sets?)69 b(One)28 b(w)m(ould)h(think)f(so|since)i (after)f(all,)i(the)0 2071 y(In\014nit)m(y)k(and)g(P)m(o)m(w)m(er)h (Set)g(Axioms)g(imply)f(the)h Fq(existenc)-5 b(e)42 b FD(of)36 b(uncoun)m(table)g(sets!)91 b(T)-8 b(o)36 b(get)h(a)f(b)s (etter)f(handle)0 2183 y(on)h(the)g(question,)i(though,)g(let's)f (examine)g(the)f(inference)h(rules)e(of)i(\014rst-order)e(logic,)40 b(b)m(y)c(whic)m(h)f(w)m(e)i(pro)m(v)m(e)0 2296 y(theorems.)71 b(W)-8 b(e)32 b(sa)m(y)f(a)g(\014rst-order)e(sen)m(tence)j(is)e Fq(valid)41 b FD(if)30 b(can)h(b)s(e)f(obtained)g(b)m(y)h(the)f(follo)m (wing)i(rules:)66 2509 y(\(1\))46 b Fi(Prop)s(ositional)36 b(Rule.)72 b FD(An)m(y)30 b(prop)s(ositional)h(tautology)h(is)f(v)-5 b(alid.)66 2697 y(\(2\))46 b Fi(Mo)s(dus)36 b(P)m(onens.)72 b FD(If)30 b Fp(A)g FD(and)g Fp(A)25 b Fn(\))h Fp(B)34 b FD(are)d(v)-5 b(alid)31 b(then)f Fp(B)35 b FD(is)30 b(v)-5 b(alid.)66 2884 y(\(3\))46 b Fi(Equalit)m(y)36 b(Rules.)76 b FD(The)31 b(follo)m(wing)i(are)f(v)-5 b(alid:)44 b(\(a\))32 b Fp(x)c FD(=)f Fp(x)p FD(,)32 b(\(b\))f Fp(x)c FD(=)g Fp(y)j FD(=)-15 b Fn(\))27 b Fp(y)j FD(=)d Fp(x)p FD(,)32 b(\(c\))h Fp(x)27 b FD(=)g Fp(y)d Fn(^)c Fp(y)30 b FD(=)227 2997 y Fp(z)g Fn(\))25 b Fp(x)g FD(=)g Fp(z)t FD(,)31 b(\(4\))g Fp(x)26 b FD(=)f Fp(y)j FD(=)-15 b Fn(\))24 b FD(\()q Fp(A)15 b FD(\()p Fp(x)p FD(\))26 b(=)-15 b Fn(\))25 b Fp(A)15 b FD(\()p Fp(y)s FD(\))q(\).)66 3185 y(\(4\))46 b Fi(Change)35 b(of)g(V)-9 b(ariables.)71 b FD(Changing)30 b(v)-5 b(ariable)31 b(names)f(lea)m(v)m(es)j(a)e (statemen)m(t)h(v)-5 b(alid.)66 3372 y(\(5\))46 b Fi(Quan)m(ti\014er)34 b(Elimination.)71 b FD(If)30 b Fn(8)p Fp(xA)15 b FD(\()p Fp(x)p FD(\))31 b(is)f(v)-5 b(alid)31 b(then)f Fp(A)15 b FD(\()q Fp(y)s FD(\))30 b(is)h(v)-5 b(alid.)66 3560 y(\(6\))46 b Fi(Quan)m(ti\014er)34 b(Addition.)72 b FD(If)29 b Fp(A)15 b FD(\()q Fp(y)s FD(\))31 b(is)f(v)-5 b(alid)31 b(where)f Fp(y)j FD(is)d(an)g(unrestricted)g(constan)m(t)i(then)e Fn(8)p Fp(xA)15 b FD(\()p Fp(x)p FD(\))31 b(is)227 3673 y(v)-5 b(alid.)66 3861 y(\(7\))46 b Fi(Quan)m(ti\014er)23 b(Rules.)58 b FD(The)20 b(follo)m(wing)h(are)g(v)-5 b(alid:)36 b(\(a\))21 b Fh(q)p Fn(8)p Fp(xA)15 b FD(\()q Fp(x)p FD(\))26 b Fn(\()-15 b(\))24 b(9)p Fp(x)p Fh(q)p Fp(A)15 b FD(\()q Fp(x)p FD(\),)23 b(\(b\))d(\()q Fp(B)k Fn(^)c(8)p Fp(xA)15 b FD(\()p Fp(x)p FD(\))q(\))25 b Fn(\()-15 b(\))227 3973 y(8)p Fp(x)15 b FD(\()p Fp(B)25 b Fn(^)20 b Fp(A)15 b FD(\()p Fp(x)p FD(\))q(\),)31 b(\(c\))g(\()p Fp(B)25 b Fn(^)20 b(9)p Fp(xA)15 b FD(\()p Fp(x)p FD(\)\))26 b Fn(\()-15 b(\))25 b(9)p Fp(x)15 b FD(\()p Fp(B)25 b Fn(^)19 b Fp(A)c FD(\()q Fp(x)p FD(\)\))q(.)141 4186 y(Ob)m(viously)-8 b(,)39 b(if)d(a)h(set)g(of)f(axioms)h(has)f(a)h(mo)s (del,)h(then)e(applying)g(the)h(inference)f(rules)g(ab)s(o)m(v)m(e)i (can)f(nev)m(er)0 4299 y(lead)31 b(to)g(a)g(con)m(tradiction.)73 b(G\177)-45 b(odel's)32 b Fq(Completeness)39 b FD(Theorem)31 b(sa)m(ys)g(the)f(con)m(v)m(erse:)43 b(w)m(e)31 b(didn't)e(acciden)m (tally)0 4412 y(lea)m(v)m(e)38 b(an)m(y)f(rules)e(out)h(of)g(the)g (list,)j(in)c(the)h(sense)g(that)h(if)f(y)m(ou)g(can't)h(get)g(a)f(con) m(tradiction)i(b)m(y)e(applying)g(the)0 4525 y(rules,)42 b(then)d(the)h(axiom)g(set)g(has)g(a)g(mo)s(del.)108 b(Equiv)-5 b(alen)m(tly)d(,)43 b(an)m(y)d(sen)m(tence)h(that's)f(true)g (in)f(all)i(mo)s(dels)e(is)0 4638 y(pro)m(v)-5 b(able.)66 b(The)26 b(Completeness)h(Theorem)f(is)g(confusing)g(for)g(t)m(w)m(o)i (reasons:)38 b(on)27 b(the)f(one)h(hand,)f(it)h(sounds)e(lik)m(e)0 4751 y(a)31 b(tautology)i(\(\\that)e(whic)m(h)g(is)f(consisten)m(t,)i (is)f(consisten)m(t"\)|what)h(could)f(it)g(p)s(ossibly)e(mean)i(to)g (pro)m(v)m(e)g(suc)m(h)0 4863 y(a)g(thing?)70 b(And)30 b(on)g(the)h(other)f(hand,)g(it)h(seems)f(to)i(con)m(tradict)g(the)e Fq(Inc)-5 b(ompleteness)40 b FD(Theorem.)141 4976 y(W)-8 b(e're)25 b(going)g(to)g(clear)f(up)f(this)h(mess,)h(and)e(as)h(a)g(b)s (on)m(us,)g(answ)m(er)g(our)f(question)h(ab)s(out)g(whether)f(all)h(mo) s(dels)0 5089 y(of)37 b(ZF)g(are)g(uncoun)m(table.)97 b(The)36 b(b)s(est)g(w)m(a)m(y)i(to)f(understand)e(the)i(Completeness)g (Theorem)g(is)g(to)g(mak)m(e)h(up)0 5202 y(a)c(consisten)m(t)h(axiom)f (set)g(that)h(y)m(ou'd)e(guess)h Fq(do)-5 b(esn)c('t)43 b FD(ha)m(v)m(e)35 b(a)f(mo)s(del.)84 b(Giv)m(en)34 b(a)g(theory)g(T,)g (let)h(Con)15 b(\(T\))34 b(b)s(e)0 5315 y(the)c(assertion)h(that)f(T)g (is)g(consisten)m(t.)61 b(W)-8 b(e)32 b(kno)m(w)e(from)f(G\177)-45 b(odel's)31 b(Incompleteness)f(Theorem)g(that)h(Con)14 b(\()q(ZF\))p eop end %%Page: 6 6 TeXDict begin 6 5 bop 0 91 a FD(can)29 b(b)s(e)f(expressed)g(in)g(ZF,)h (and)f(also)h(that)g(Con)15 b(\(ZF\))29 b(can't)g(b)s(e)f Fq(pr)-5 b(ove)g(d)40 b FD(in)28 b(ZF,)h(assuming)f(ZF)g(is)h (consisten)m(t.)3859 58 y Fy(5)0 204 y FD(It)42 b(follo)m(ws)h(that)f (assuming)f(ZF)h(is)g(consisten)m(t,)k(the)c(\\self-hating)h(theory")f (ZF)15 b(+)p Fh(q)g FD(Con)g(\()q(ZF\),)45 b(or)c(ZF)h(plus)0 317 y(the)30 b(assertion)h(of)f(its)g(o)m(wn)g(inconsistency)-8 b(,)31 b(m)m(ust)f(also)g(b)s(e)g(consisten)m(t.)71 b(So)30 b(b)m(y)g(the)g(Completeness)g(Theorem,)0 430 y(ZF)15 b(+)p Fh(q)g FD(Con)g(\(ZF\))25 b(has)f(a)g(mo)s(del.)63 b(What)25 b(on)f(earth)h(could)f(it)h(b)s(e?)62 b(W)-8 b(e'll)26 b(answ)m(er)e(this)g(question)g(via)h(a)g(\014ctional)0 543 y(dialogue)32 b(b)s(et)m(w)m(een)f(y)m(ou)f(and)g(the)h(axioms)g (of)f(ZF)15 b(+)p Fh(q)g FD(Con)g(\()q(ZF\).)141 681 y Fi(Y)-9 b(ou:)50 b FD(Lo)s(ok,)36 b(y)m(ou)f(sa)m(y)g(ZF)g(is)g (inconsisten)m(t,)i(from)d(whic)m(h)g(it)h(follo)m(ws)h(that)g(there's) f(a)g(pro)s(of)e(in)i(ZF)f(that)0 794 y(1)21 b(+)f(1)25 b(=)g(3.)72 b(Ma)m(y)31 b(I)f(see)h(that)g(pro)s(of)7 b(?)141 907 y Fi(Axioms)32 b(of)41 b FD(ZF)15 b(+)p Fh(q)g FD(Con)g(\(ZF\))q Fi(:)38 b FD(I)27 b(prefer)f(to)i(talk)g(ab)s(out)f (in)m(tegers)h(that)f(enco)s(de)g(pro)s(ofs.)66 b(\(Actually)29 b Fq(sets)0 1020 y FD(that)i(enco)s(de)f(in)m(tegers)i(that)f(enco)s (de)g(pro)s(ofs.)70 b(But)30 b(I'll)h(cut)g(y)m(ou)f(a)h(break|y)m (ou're)g(only)g(h)m(uman,)e(after)i(all.\))141 1132 y Fi(Y)-9 b(ou:)41 b FD(Then)30 b(sho)m(w)g(me)g(the)h(in)m(teger.)141 1245 y Fi(Axioms:)41 b FD(OK,)30 b(here)h(it)g(is:)40 b Fp(X)7 b FD(.)141 1358 y Fi(Y)-9 b(ou:)41 b FD(What)31 b(the)g(hell)g(is)f Fp(X)7 b FD(?)141 1471 y Fi(Axioms:)41 b FD(It's)31 b(just)f Fp(X)7 b FD(,)31 b(the)f(in)m(teger)i(enco)s(ded) e(b)m(y)g(a)h(set)g(in)f(the)h(univ)m(erse)f(that)h(I)f(describ)s(e.) 141 1584 y Fi(Y)-9 b(ou:)41 b FD(But)31 b(what)f(is)h Fp(X)7 b FD(,)31 b(as)f(an)g Fq(or)-5 b(dinary)35 b(inte)-5 b(ger)10 b FD(?)141 1697 y Fi(Axioms:)41 b FD(No,)32 b(no,)e(no!)71 b(T)-8 b(alk)31 b(to)g(the)g(axioms.)141 1810 y Fi(Y)-9 b(ou:)41 b FD(Alrigh)m(t,)32 b(let)f(me)g(ask)f(y)m(ou)h (ab)s(out)f Fp(X)7 b FD(.)72 b(Is)29 b(greater)j(or)e(smaller)h(than)f (a)h(billion?)141 1923 y Fi(Axioms:)41 b FD(Greater.)141 2036 y Fi(Y)-9 b(ou:)41 b FD(The)30 b(10)668 2003 y Fy(10)738 1979 y Fu(1)p Fg(;)p Fu(000)p Fg(;)p Fu(000)p Fg(;)p Fu(000)1109 2036 y FD(th)g(Ac)m(k)m(ermann)h(n)m(um)m(b)s(er?)141 2149 y Fi(Axioms:)41 b FD(Greater)32 b(than)e(that)h(to)s(o.)141 2262 y Fi(Y)-9 b(ou:)41 b FD(What's)31 b Fp(X)789 2229 y Fy(2)850 2262 y FD(+)19 b(100?)141 2374 y Fi(Axioms:)41 b FD(Hmm,)31 b(let)g(me)f(see.)17 b(.)e(.)46 b Fp(Y)20 b FD(.)141 2487 y Fi(Y)-9 b(ou:)45 b FD(Wh)m(y)33 b(can't)g(I)f(just)f (add)h(an)g(axiom)h(to)g(rule)f(out)h(these)f(w)m(eird)g(`nonstandard)f (in)m(tegers?')80 b(Let)33 b(me)0 2600 y(try:)41 b(for)30 b(all)h(in)m(tegers)h Fp(X)7 b FD(,)31 b Fp(X)37 b FD(b)s(elongs)31 b(to)g(the)f(set)h(obtained)g(b)m(y)f(starting)h(from)f(0)h(and...)141 2713 y Fi(Axioms:)44 b FD(Ha)32 b(ha!)76 b(This)30 b(is)i (\014rst-order)f(logic.)77 b(Y)-8 b(ou're)32 b(not)g(allo)m(w)m(ed)i (to)e(talk)g(ab)s(out)g(sets)g(of)f(ob)5 b(jects|)0 2826 y(ev)m(en)31 b(if)f(the)h(ob)5 b(jects)31 b(are)g Fq(themselves)38 b FD(sets.)141 2939 y Fi(Y)-9 b(ou:)41 b FD(Argh!)71 b(I)30 b(kno)m(w)g(y)m(ou're)h(lying)g(ab)s(out)f(this)h(pro)s(of)e (that)i(1)21 b(+)f(1)25 b(=)g(3,)31 b(but)f(I'll)h(nev)m(er)g(catc)m(h) h(y)m(ou.)141 3052 y Fi(Axioms:)61 b FD(That)40 b(righ)m(t!)111 b(What)41 b(G\177)-45 b(odel)41 b(sho)m(w)m(ed)f(is)g(that)h(w)m(e)g (can)f(k)m(eep)h(pla)m(ying)g(this)f(game)h(forev)m(er.)0 3165 y(What's)36 b(more,)i(the)d(in\014nite)h(sequence)g(of)g(bizarre)f (en)m(tities)j(y)m(ou'd)d(force)i(me)e(to)i(mak)m(e)f(up|)p Fp(X)7 b FD(,)37 b Fp(Y)20 b FD(,)37 b(and)e(so)0 3278 y(on|w)m(ould)30 b(then)g(constitute)i(a)f Fq(mo)-5 b(del)41 b FD(for)30 b(the)h(prep)s(osterous)e(theory)i(ZF)15 b(+)p Fh(q)g FD(Con)g(\(ZF\).)141 3391 y Fi(Y)-9 b(ou:)41 b FD(But)31 b(ho)m(w)f(do)g(y)m(ou)h(kno)m(w)g(I'll)f(nev)m(er)h(trap)f (y)m(ou)h(in)f(an)g(inconsistency?)141 3504 y Fi(Axioms:)43 b FD(Because)32 b(if)f(y)m(ou)h(did,)e(the)i(Completeness)f(Theorem)g (sa)m(ys)g(that)h(w)m(e)g(could)f(con)m(v)m(ert)h(that)g(in)m(to)0 3616 y(an)g(inconsistency)h(in)f(the)g(original)h(axioms,)h(whic)m(h)e (con)m(tradicts)i(the)e(ob)m(vious)h(fact)g(that)f(ZF)g(is)h (consis|no,)0 3729 y(w)m(ait!)72 b(I'm)30 b(not)h(supp)s(osed)d(to)j (kno)m(w)g(that!)71 b(Aaahh!)h Fq([The)32 b(axioms)i(melt)f(in)g(a)g (pudd)5 b(le)33 b(of)g(inc)-5 b(onsistency.])141 3867 y FD(As)45 b(a)g(corollary)h(of)f(G\177)-45 b(odel's)45 b(Completeness)g(Theorem,)k(w)m(e)c(get)h(the)e Fq(L\177)-46 b(owenheim-Skolem)48 b(The)-5 b(or)g(em)p FD(,)0 3980 y(whic)m(h)26 b(actually)j(predates)d(G\177)-45 b(odel:)40 b(if)27 b(a)g(theory)g(T)f(has)g(a)h(mo)s(del,)h(then)e(it)h(has)g(a)g (mo)s(del)f(of)h(at)h(most)f(coun)m(table)0 4093 y(cardinalit)m(y)-8 b(.)79 b(Wh)m(y?)109 b(Because)33 b(the)g(game)g(ab)s(o)m(v)m(e|where)f (w)m(e)h(k)m(eep)f(c)m(hallenging)i(T)d(to)i(name)f(the)g(ob)5 b(jects)0 4206 y(it)39 b(sa)m(ys)h(exist,)i(and)c(T)h(resp)s(onds)e(b)m (y)h(`co)s(oking)i(new)f(ob)5 b(jects)39 b(to)h(order'|lasts)f(at)h (most)f(coun)m(tably)h(man)m(y)0 4319 y(steps,)34 b(since)g(eac)m(h)g (`c)m(hallenge')i(can)e(b)s(e)f(expressed)g(as)h(a)g(\014nite)f (string.)84 b(And)33 b(the)g(Completeness)h(Theorem)0 4432 y(guaran)m(tees)e(that)f(the)f(\014nal)g(result)h(will)f(b)s(e)g (a)h(mo)s(del)f(for)g(T,)g(assuming)g(T)g(w)m(as)h(consisten)m(t.)141 4545 y(In)25 b(fact,)j(it's)e(kno)m(wn)g(that)g(an)m(y)g(theory)g(that) h(has)e(arbitrarily)h(large)h(\014nite)f(mo)s(dels)f(has)h(an)f (in\014nite)h(mo)s(del,)0 4658 y(and)38 b(an)m(y)h(theory)h(that)f(has) g(an)f(in\014nite)h(mo)s(del)g(has)f(mo)s(dels)h(of)g(whatev)m(er)h (in\014nite)e(cardinalit)m(y)i(w)m(e)g(w)m(an)m(t.)0 4770 y(This)c(is)h(already)g(a)g(tip-o\013)g(that)h(the)f (\014rst-order)e(sen)m(tences)j(game)g(can't)g(answ)m(er)e(an)m(y)h (question)g(w)m(e)g(migh)m(t)0 4883 y(ask.)71 b(It)31 b(can't)g(ev)m(en)g(tell)h(us)d(ho)m(w)i(man)m(y)f(ob)5 b(jects)31 b(are)g(in)f(the)h(univ)m(erse!)p 0 4962 1560 4 v 104 5016 a Fu(5)138 5048 y Ft(F)-6 b(or)32 b(supp)r(ose)g(Con)13 b(\(ZF\))32 b(could)f(b)r(e)h(pro)n(v)n(ed)f(in)g(ZF.)84 b(It's)32 b(easy)g(to)g(pro)n(v)n(e)f(in)h(ZF)f(that)h(Con)13 b(\(ZF\))32 b(implies)g(G)13 b(\(ZF\),)34 b(where)0 5139 y(G)13 b(\(ZF\))24 b(is)h(the)g(famous)g(G\177)-38 b(odel)26 b(sen)n(tence)e(that)g(sa)n(ys)h(\\I)g(am)g(not)f(pro)n(v)l(able)g(in)h (ZF.")50 b(But)24 b(then)g(w)n(e)h(w)n(ould)g(ha)n(v)n(e)f(a)h(pro)r (of)g(in)g(ZF)f(of)0 5231 y(G)13 b(\(ZF\),)26 b(so)g(ZF)g(w)n(ould)g(b) r(e)f(inconsisten)n(t.)61 b(\(Indeed,)25 b(Con)13 b(\(ZF\))25 b(and)h(G)13 b(\(ZF\))25 b(are)h(easily)h(seen)f(to)g(b)r(e)f(equiv)l (alen)n(t.\))p eop end %%Page: 7 7 TeXDict begin 7 6 bop 0 91 a Fj(2.2)112 b(Pro)m(ving)38 b(Indep)s(endence)0 263 y FD(Mo)m(ving)44 b(closer)g(to)g(the)f(sub)5 b(ject)43 b(of)g(the)g(surv)m(ey)-8 b(,)47 b(ho)m(w)c(do)s(es)f(one)i (pro)m(v)m(e)f(a)h(statemen)m(t)h(indep)s(enden)m(t)c(of)j(a)0 376 y(\014rst-order)25 b(theory?)66 b(There)26 b(are)g(actually)i(t)m (w)m(o)g(metho)s(ds:)38 b Fq(c)-5 b(onsistency)30 b(str)-5 b(ength)p FD(,)28 b(and)e Fq(r)-5 b(elative)30 b(c)-5 b(onsistency)p FD(.)141 489 y(Let's)35 b(start)h(with)e(consistency)h (strength.)89 b(If)34 b(w)m(e)h(remo)m(v)m(e)h(the)f(Axiom)g(of)g (In\014nit)m(y)f(from)g(ZF,)h(w)m(e)g(get)h(a)0 602 y(theory)c(equiv)-5 b(alen)m(t)33 b(to)f(P)m(eano)g(Arithmetic)h(\(P)-8 b(A\).)76 b(No)m(w,)33 b(it's)f(not)f(hard)g(to)h(see)g(that)g(ZF)27 b Fh(\017)f FD(Con)15 b(\(P)-8 b(A)q(\);)32 b(that)0 715 y(is,)g(Con)15 b(\(P)-8 b(A)q(\))32 b(is)g(a)g(theorem)g(of)g(ZF.) 76 b(The)32 b(reason)f(is)h(that)h(in)e(ZF,)h(there)g(exist)h (in\014nite)e(sets|for)h(example,)0 827 y(the)j(set)g(of)f(all)i (\014nite)e(sets|that)i(w)m(e)e(can)h(tak)m(e)h(as)f(mo)s(dels)f(for)g (P)-8 b(A)q(.)87 b(On)34 b(the)g(other)h(hand,)g(G\177)-45 b(odel)35 b(tells)h(us)0 940 y(that)e(ZF)29 b Fn(6)p Fh(\017)g FD(Con)15 b(\(ZF\))q(.)81 b(If)33 b(w)m(e)g(w)m(an)m(t)h(to)g (pro)m(v)m(e)g(Con)14 b(\()q(ZF\),)34 b(w)m(e)f(ha)m(v)m(e)i(to)e(p)s (ostulate)h(an)f(in\014nit)m(y)g(bigger)g(than)0 1053 y(an)m(ything)i(de\014nable)e(in)h(ZF|a)h(so-called)h(`large)f (cardinal.')87 b(\(When)35 b(set)f(theorists)h(sa)m(y)g(large,)i(they)d Fq(me)-5 b(an)0 1166 y FD(large.\))76 b(If)31 b(LC)f(asserts)i(the)f (existence)i(of)e(suc)m(h)g(a)h(cardinal,)g(then)e(ZF)15 b(+)g(LC)26 b Fh(\017)h FD(Con)14 b(\()q(ZF\).)74 b(So)31 b(w)m(e)h(can)f(rank)0 1279 y(the)g(theories)h(in)f(a)g(`consistency)i (strength)e(hierarc)m(h)m(y)-8 b(,')33 b(from)d(P)-8 b(A)32 b(to)g(ZF)f(to)g(ZF)15 b(+)g(LC.)74 b(Notice)33 b(that)e(in)g(P)-8 b(A)q(,)0 1392 y(w)m(e)34 b(can't)h(ev)m(en)f(pro)m (v)m(e)g(that)h(Con)14 b(\()q(P)-8 b(A\))31 b(=)-15 b Fn(\))30 b FD(Con)15 b(\()q(ZF)o(\))q(.)84 b(F)-8 b(or)34 b(then)g(w)m(e)g(could)f(also)i(pro)m(v)m(e)f(that)h(in)e(ZF,)i(and)0 1505 y(since)c(ZF)25 b Fh(\017)g FD(Con)14 b(\()q(P)-8 b(A\))q(,)30 b(w)m(e'd)h(ha)m(v)m(e)g(ZF)26 b Fh(\017)e FD(Con)15 b(\(ZF\))q(,)30 b(con)m(tradiction.)141 1618 y(In)j(general,)i(to)e(sho)m(w)g(that)h(a)g(statemen)m(t)h(is)e(unpro)m (v)-5 b(able)33 b(in)f(some)i(theory)-8 b(,)35 b(w)m(e)e(argue)h(that)f (if)h(it)f(w)m(asn't,)0 1731 y(then)j(w)m(e)h(could)g(collapse)h(t)m(w) m(o)g(lev)m(els)g(of)f(the)g(consistency)g(strength)g(hierarc)m(h)m (y|and)f(thereb)m(y)h(violate)i(the)0 1844 y(Incompleteness)k(Theorem.) 121 b(As)43 b(another)g(application,)48 b(y)m(ou)43 b(migh)m(t)h(w)m (onder:)65 b(supp)s(ose)42 b FC(P)k Fn(6)p FD(=)g FC(NP)d FD(w)m(ere)0 1957 y(unpro)m(v)-5 b(able)40 b(in)g(a)h(formal)g(system)g (suc)m(h)f(as)h(ZF.)112 b(Ma)m(yb)s(e)41 b(w)m(e)h(could)e(still)i(pro) m(v)m(e)f FC(P)i Fn(6)p FD(=)f FC(NP)f FD(b)m(y)f Fq(assuming)0 2070 y FD(from)31 b(the)h(outset)h(\(that)g(is,)f(adding)g(as)g(an)f (axiom\))i(that)g(ZF)e(do)s(es)h(pro)m(v)m(e)h FC(P)27 b Fn(6)p FD(=)h FC(NP)p FD(?)76 b(A)32 b(result)g(called)h(L\177)-45 b(ob's)0 2182 y(Theorem)41 b(uses)f(consistency)i(strength)f(to)g(rule) g(out)g(this)g(strange)g(p)s(ossibilit)m(y)-8 b(.)114 b(\(I)41 b(prefer)f(to)i(call)g(it)g(the)0 2295 y(\\Y)-8 b(ou-Had-The-Mo)5 b(jo-All-Along)35 b(Theorem."\))0 2475 y Fi(Theorem)g(1)g(\(L\177)-52 b(ob\))45 b Fq(If)37 b(sentenc)-5 b(e)36 b Fp(A)h Fq(c)-5 b(an)37 b(b)-5 b(e)37 b(pr)-5 b(oven)38 b(in)e FD(ZF)15 b(+)g(\()q(ZF)25 b Fh(\017)g Fp(A)p FD(\))p Fq(,)38 b(then)f(it)f(c)-5 b(an)38 b(also)g(b)-5 b(e)36 b(pr)-5 b(oven)38 b(in)0 2588 y FD(ZF)32 b Fq(alone.)141 2767 y Fi(Pro)s(of.)63 b FD(If)38 b(ZF)f(is)h(inconsisten)m(t)g(then)g (it)g(can)g(pro)m(v)m(e)g(an)m(ything,)j(so)c(assume)h(Con)15 b(\(ZF\).)100 b(Supp)s(ose)36 b(ZF)0 2880 y(pro)m(v)m(es)24 b(\(ZF)h Fh(\017)g Fp(A)p FD(\))h(=)-15 b Fn(\))25 b Fp(A)p FD(.)61 b(Then)23 b(ZF)15 b(+)p Fh(q)p Fp(A)25 b Fh(\017)g FD(\(ZF)g Fn(6)p Fh(\017)g Fp(A)p FD(\))q(.)61 b(Supp)s(ose)22 b(also)i(that)g(w)m(e)f Fq(ne)-5 b(e)g(d)34 b FD(the)23 b(axiom)h(\()q(ZF)h Fh(\017)f Fp(A)p FD(\))0 2993 y(to)35 b(pro)m(v)m(e)f Fp(A)p FD(|that)h(is,)g(that)f(ZF)d Fn(6)p Fh(\017)g Fp(A)p FD(.)85 b(Then)33 b(since)h(ZF)g(is)g (consisten)m(t,)i(ZF)15 b(+)p Fh(q)p Fp(A)35 b FD(is)e(also)i (consisten)m(t.)87 b(But)0 3106 y(ZF)15 b(+)p Fh(q)p Fp(A)29 b FD(pro)m(v)m(es)g(ZF)d Fn(6)p Fh(\017)e Fp(A)p FD(,)30 b(whic)m(h)e(is)h(equiv)-5 b(alen)m(t)30 b(to)f(Con)15 b(\()q(ZF)g(+)p Fh(q)p Fp(A)p FD(\).)69 b(So)29 b(ZF)15 b(+)p Fh(q)p Fp(A)25 b Fh(\017)g FD(Con)15 b(\(ZF)g(+)p Fh(q)p Fp(A)p FD(\))q(,)29 b(whic)m(h)0 3219 y(con)m(tradicts)j(the)e (consistency)i(of)e(ZF)15 b(+)p Fh(q)p Fp(A)p FD(.)p 1617 3219 46 46 v 141 3332 a(The)41 b(other)g(metho)s(d)f(for)h(pro)m (ving)g(indep)s(endence)f(is)h Fq(r)-5 b(elative)43 b(c)-5 b(onsistency)p FD(.)114 b(As)41 b(Shelah)g([59)q(])g(put)f(it,)0 3444 y(consistency)28 b(strength)e(mak)m(es)i(the)f(univ)m(erse)g(of)g (logical)i(theories)e(`taller,')j(while)d(relativ)m(e)h(consistency)g (mak)m(es)0 3557 y(it)c(`fatter.')62 b(Relativ)m(e)26 b(consistency)e(w)m(as)f(what)g(G\177)-45 b(odel)24 b([20)q(])g(and)e (Cohen)h([13)q(])g(used)f(to)i(pro)m(v)m(e)g(the)f(indep)s(endence)0 3670 y(of)36 b(the)g(Axiom)g(of)g(Choice)h(\(A)m(C\))g(and)e(Con)m(tin) m(uum)g(Hyp)s(othesis)h(\(CH\))g(from)f(ZF.)72 b(Recall)37 b(that)g(A)m(C)f(is)g(the)0 3783 y(assertion)24 b(that,)h(giv)m(en)f(a) f(set)h Fp(x)f FD(of)g(nonempt)m(y)-8 b(,)25 b(pairwise)e(disjoin)m(t)g (sets,)i(there)e(exists)h(a)f(set)h(that)g(shares)e(exactly)0 3896 y(one)30 b(elemen)m(t)h(with)e(eac)m(h)h(set)g(in)f Fp(x)p FD(.)70 b(CH)29 b(is)g(the)h(assertion)g(that)g(there's)g(no)f (set)h(of)f(in)m(termediate)j(cardinalit)m(y)0 4009 y(b)s(et)m(w)m(een) f(the)g(in)m(tegers)g(and)f(the)h(sets)f(of)h(in)m(tegers.)72 b(Then)29 b(G\177)-45 b(odel)32 b(pro)m(v)m(ed)e(that)968 4180 y(Con)15 b(\(ZF\))26 b(=)-15 b Fn(\))25 b FD(\(Con)15 b(\(ZF)g(+)g(A)m(C\))21 b Fn(^)f FD(Con)14 b(\()q(ZF)h(+)g(CH\)\))g Fp(;)0 4351 y FD(while)30 b(Cohen)g(pro)m(v)m(ed)h(that)903 4522 y(Con)15 b(\(ZF\))26 b(=)-15 b Fn(\))24 b FD(\()q(Con)15 b(\(ZF)g(+)p Fh(q)g FD(A)m(C)q(\))20 b Fn(^)g FD(Con)15 b(\(ZF)g(+)p Fh(q)g FD(CH\))q(\))g Fp(:)2957 4489 y Fy(6)0 4693 y FD(In)20 b(other)i(w)m(ords,)h(b)m(y)e Fq(starting)30 b FD(with)21 b(a)g(mo)s(del)g(for)g(ZF,)i(w)m(e)f(get)g(another)g(mo)s (del)f(for)g(ZF)g(with)g(sp)s(eci\014c)g(prop)s(erties)0 4806 y(w)m(e)j(w)m(an)m(t|for)h(example,)h(that)e(CH)g(is)f(true,)i(or) f(that)h(A)m(C)f(is)f(false.)63 b(F)-8 b(or)25 b(this)e(reason,)j(it's) e(clear)h(that)g(Con)14 b(\()q(ZF\))0 4919 y(is)30 b(not)h(a)g(theorem) g(of,)f(sa)m(y)-8 b(,)32 b(ZF)15 b(+)g(CH|for)30 b(if)g(it)h(w)m(ere,)g (then)f(w)m(e'd)h(ha)m(v)m(e)1403 5090 y(ZF)15 b(+)g(CH)25 b Fh(\017)g FD(Con)15 b(\(ZF)g(+)g(CH\))g Fp(;)p 0 5163 1560 4 v 104 5217 a Fu(6)138 5249 y Ft(Am)n(usingly)-6 b(,)34 b(b)r(oth)e(of)i(these)e(implications)j(are)e(actually)g (theorems)g(of)g(P)-6 b(A|since)33 b(to)g(pro)n(v)n(e)f(them,)i(one)f (ultimately)g(just)0 5340 y(talks)26 b(ab)r(out)g(axioms,)h(whic)n(h)e (are)i(\014nite)e(strings)h(of)h(sym)n(b)r(ols.)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 0 91 a FD(therefore)27 b(ZF)15 b(+)g(CH)27 b(w)m(ould)g(b)s(e)f(inconsisten)m(t,)j(therefore)e(ZF)g (itself)h(w)m(ould)e(b)s(e)h(inconsisten)m(t.)67 b(So)27 b(unlik)m(e)g(with)0 204 y(the)g(metho)s(d)g(of)g(consistency)h (strength,)g(adding)e(CH)h(do)s(esn't)g(lead)h(to)f(a)h(`stronger')f (theory|just)g(a)g(di\013eren)m(t)0 317 y(one.)141 430 y(In)d(summary)-8 b(,)25 b(then,)g(if)f(w)m(e)h(w)m(an)m(ted)g(to)g (pro)m(v)m(e)g(that)g FC(P)h Fn(6)p FD(=)f FC(NP)f FD(\(or)h FC(P)g FD(=)g FC(NP)q FD(\))f(is)h(unpro)m(v)-5 b(able)23 b(in)h(some)h(theory)-8 b(,)0 543 y(there)31 b(are)f(t)m(w)m(o)i(w)m(a) m(ys)f(w)m(e)g(migh)m(t)g(go)g(ab)s(out)g(it:)41 b(consistency)31 b(strength)f(or)h(relativ)m(e)h(consistency)-8 b(.)0 829 y FE(3)135 b(Early)46 b(Results)0 1032 y FD(With)d(the)g(logic)h (bac)m(kground)e(out)h(of)g(the)f(w)m(a)m(y)-8 b(,)48 b(it's)43 b(\014nally)f(time)h(to)h(sa)m(y)f(something)g(ab)s(out)f FC(P)h FD(vs.)f FC(NP)q FD(.)0 1145 y(W)-8 b(e'll)35 b(start)f(with)g(some)f(results)h(from)f(the)g(sev)m(en)m(ties)j(and)c (eigh)m(ties:)49 b(in)33 b(Section)i(3.1,)g(oracle)g(indep)s(endence)0 1258 y(theorems)f(due)f(to)h(Hartmanis)g(and)f(Hop)s(croft)g([26)q(])h (and)f(Hartmanis)h([25)q(];)i(and)d(in)g(Section)h(3.2,)i(non-oracle)0 1371 y(indep)s(endence)42 b(theorems)i(\(concerning)g(w)m(eak)g (logical)i(theories\))e(due)f(to)h(DeMillo)i(and)d(Lipton)g([15)q(])h (and)0 1484 y(Sazano)m(v)32 b([58)q(].)0 1727 y Fj(3.1)112 b(Oracles)0 1899 y FD(Giv)m(en)31 b(a)g(T)-8 b(uring)30 b(mac)m(hine)i Fp(M)10 b FD(,)31 b(let)g Fp(L)15 b FD(\()p Fp(M)10 b FD(\))31 b(b)s(e)f(the)h(language)h(accepted)g(b)m(y)f Fp(M)10 b FD(.)71 b(The)31 b(follo)m(wing)h(w)m(as)f(sho)m(wn)0 2012 y(in)f([24)q(,)h(26)q(].)0 2224 y Fi(Theorem)k(2)g (\(Hartmanis-Hop)s(croft\))45 b Fq(Ther)-5 b(e)26 b(exists)g(a)g(T)-7 b(uring)25 b(machine)i Fp(M)35 b Fq(that)27 b(halts)g(on)f(every)g (input,)0 2337 y(such)k(that)h(r)-5 b(elative)31 b(to)f(the)h(or)-5 b(acle)31 b Fp(L)15 b FD(\()p Fp(M)10 b FD(\))q Fq(,)30 b(neither)g FC(P)c FD(=)f FC(NP)30 b Fq(nor)h FC(P)25 b Fn(6)p FD(=)g FC(NP)30 b Fq(is)g(pr)-5 b(ovable)32 b(in)d FD(ZF)p Fq(,)i(assuming)f FD(ZF)0 2450 y Fq(is)j(c)-5 b(onsistent.)141 2663 y Fi(Pro)s(of.)40 b FD(The)26 b(language)i Fp(L)15 b FD(\()p Fp(M)10 b FD(\))27 b(will)g(turn)e(out)i(to)g(b)s(e)f (the)g(empt)m(y)h(set)g(\(that)h(is,)f Fp(M)37 b FD(alw)m(a)m(ys)28 b(rejects\).)66 b(The)0 2776 y(catc)m(h)27 b(is)f(that)g(its)g (emptiness)g(can't)g(b)s(e)f Fq(pr)-5 b(oven)34 b FD(in)25 b(ZF.)65 b(Here's)26 b(ho)m(w)g(it)g(w)m(orks:)38 b(b)m(y)26 b(Bak)m(er,)i(Gill,)g(and)d(Solo)m(v)-5 b(a)m(y)0 2889 y([4)q(],)42 b(there)e(exists)h(an)e(oracle)j Fp(A)d FD(relativ)m(e)j(to)f(whic)m(h)e FC(P)i FD(=)g FC(NP)p FD(,)f(and)f(another)h(oracle)i Fp(B)i FD(relativ)m(e)e(to)e(whic)m(h)0 3002 y FC(P)32 b Fn(6)p FD(=)f FC(NP)p FD(.)339 2969 y Fy(7)465 3002 y FD(Both)j(of)h(these)f(oracles)i(are)e(computable.)87 b(Let)35 b Fp(M)2322 3016 y Fy(1)2361 3002 y Fp(;)15 b(M)2489 3016 y Fy(2)2529 3002 y Fp(;)g(:)g(:)g(:)36 b FD(b)s(e)d(a)i(standard)e(en)m(umeration)i(of)0 3114 y(T)-8 b(uring)32 b(mac)m(hines,)i(and)f(let)g Fp(P)1089 3128 y Fy(1)1129 3114 y Fp(;)15 b(P)1227 3128 y Fy(2)1267 3114 y Fp(;)g(:)g(:)g(:)35 b FD(b)s(e)d(a)h(standard)f(en)m(umeration)h (of)g(ZF)g(pro)s(ofs.)80 b(Then)32 b(w)m(e)h(de\014ne)f Fp(M)0 3227 y FD(as)f(follo)m(ws:)41 b(giv)m(en)32 b(an)e(in)m(teger)i Fp(x)e FD(as)h(input,)e Fp(M)41 b FD(accepts)31 b(if)g(either)66 3440 y(\(1\))46 b(There's)30 b(a)h(pro)s(of)f(that)h FC(P)1120 3407 y Fo(L)p Fy(\()p Fo(M)7 b Fy(\))1327 3440 y FD(=)25 b FC(NP)1545 3403 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))1757 3440 y FD(among)31 b Fp(P)2108 3454 y Fy(1)2148 3440 y Fp(;)15 b(:)g(:)g(:)i(;)e(P)2408 3454 y Fo(x)2452 3440 y FD(,)31 b(and)f Fp(x)25 b Fn(2)g Fp(B)5 b FD(;)30 b(or)66 3628 y(\(2\))46 b(There's)30 b(a)h(pro)s(of)f(that)h FC(P)1120 3595 y Fo(L)p Fy(\()p Fo(M)7 b Fy(\))1327 3628 y Fn(6)p FD(=)25 b FC(NP)1545 3591 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))1757 3628 y FD(among)31 b Fp(P)2108 3642 y Fy(1)2148 3628 y Fp(;)15 b(:)g(:)g(:)i(;)e(P)2408 3642 y Fo(x)2452 3628 y FD(,)31 b(and)f Fp(x)25 b Fn(2)g Fp(A)p FD(.)141 3840 y(Y)-8 b(ou)42 b(migh)m(t)g(complain)g(that)g(w)m(e)f(used)g Fp(M)51 b FD(in)41 b(the)h(de\014nition)f(of)g Fp(M)10 b FD(.)115 b(What)42 b(justi\014es)f(this,)j(though,)0 3953 y(is)35 b(the)g(Recursion)f(Theorem,)i(whic)m(h)e(sa)m(ys)h(that)h (w)m(e)f(can)g(alw)m(a)m(ys)h(assume)e(without)h(loss)g(of)g(generalit) m(y)h(that)0 4066 y(a)j(program)f(has)g(access)i(to)f(its)g(o)m(wn)f (co)s(de.)104 b(The)38 b(idea)h(is)f(a)h(generalization)i(of)e(the)f (famous)g(self-prin)m(ting)0 4179 y(program:)141 4292 y FB(Print)46 b(the)h(following)f(twice,)g(the)h(second)f(time)g(in)i (quotes.)141 4405 y(``Print)e(the)h(following)e(twice,)h(the)h(second)f (time)h(in)g(quotes.'')141 4518 y FD(No)m(w)35 b(supp)s(ose)d(there)i (exists)g(a)g(ZF)f(pro)s(of)g(that)i FC(P)1914 4485 y Fo(L)p Fy(\()p Fo(M)7 b Fy(\))2126 4518 y FD(=)31 b FC(NP)2350 4481 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))2532 4518 y FD(.)84 b(Then)33 b(b)s(ey)m(ond)g(some)h(\014nite)g(p)s(oin)m(t,)0 4630 y(the)g(oracle)g Fp(L)15 b FD(\()q Fp(M)10 b FD(\))33 b(equals)h Fp(B)5 b FD(,)34 b(and)f(th)m(us)g FC(P)1557 4597 y Fo(L)p Fy(\()p Fo(M)7 b Fy(\))1769 4630 y Fn(6)p FD(=)30 b FC(NP)1992 4594 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))2174 4630 y FD(.)83 b(Similarly)-8 b(,)35 b(if)e(there)h(exists)g(a)g(ZF)f (pro)s(of)f(that)0 4743 y FC(P)58 4710 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))267 4743 y Fn(6)p FD(=)26 b FC(NP)486 4707 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))668 4743 y FD(,)32 b(then)f(b)s(ey)m(ond)f(some)i(\014nite)f(p)s(oin)m(t)g Fp(L)15 b FD(\()q Fp(M)10 b FD(\))31 b(equals)h Fp(A)p FD(,)g(and)e(th)m(us)h FC(P)3064 4710 y Fo(L)p Fy(\()q Fo(M)7 b Fy(\))3273 4743 y FD(=)26 b FC(NP)3493 4707 y Fo(L)p Fy(\()p Fo(M)7 b Fy(\))3674 4743 y FD(.)75 b(W)-8 b(e)0 4856 y(conclude)31 b(that)g(assuming)f(ZF)g(is)g(consisten)m(t,)i (there)f(is)f(no)h(ZF)f(pro)s(of)f(of)i(either)g(statemen)m(t.)p 3333 4856 46 46 v 141 4969 a(The)h(Hartmanis-Hop)s(croft)i(theorem)f (is)f(called)i(`represen)m(tation-dep)s(enden)m(t,')g(since)f(the)g (indep)s(endence)0 5082 y(really)h(relies)g(on)e(the)i(T)-8 b(uring)32 b(mac)m(hine)i Fp(M)43 b FD(b)m(y)33 b(whic)m(h)f(w)m(e're)i Fq(told)44 b FD(ab)s(out)32 b(the)i(oracle,)h(not)e(the)g(oracle)i (itself.)p 0 5161 1560 4 v 104 5215 a Fu(7)138 5247 y Ft(Basically)-6 b(,)37 b Fr(A)32 b Ft(is)i(just)f(a)g Fs(PSP)-6 b(A)n(CE)p Ft(-complete)33 b(language,)k(whic)n(h)c (collapses)i(b)r(oth)d Fs(P)h Ft(and)g Fs(NP)g Ft(to)g Fs(PSP)-6 b(A)n(CE)p Ft(;)37 b(while)d Fr(B)i Ft(is)e(an)0 5338 y(in\014nite)25 b(sequence)h(of)g(hard)f(searc)n(h)i(problems,)f (constructed)g(b)n(y)e(diagonalizing)k(o)n(v)n(er)e(all)g(p)r (olynomial-time)h(T)-6 b(uring)26 b(mac)n(hines.)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 0 91 a FD(If)29 b(someone)i(told)f(us)f(that)h Fp(L)15 b FD(\()p Fp(M)10 b FD(\))30 b(w)m(as)g(empt)m(y)-8 b(,)31 b(then)e(w)m(e'd)h(b)s(e)f(bac)m(k)h(to)h(the)e(standard)g (\(unrelativized\))i FC(P)f FD(vs.)0 204 y FC(NP)g FD(question,)g(whic) m(h)f(of)h(course)f(isn't)h(kno)m(wn)f(to)h(b)s(e)f(indep)s(enden)m(t)f (of)h(ZF.)70 b(So)29 b(y)m(ou)h(migh)m(t)g(w)m(onder:)40 b(can)29 b(w)m(e)0 317 y(construct)37 b(a)g(computable)g(oracle)g Fn(O)s FD(,)h(suc)m(h)f(that)g FC(P)1863 284 y Ff(O)1961 317 y FD(vs.)g FC(NP)2229 280 y Ff(O)2327 317 y FD(is)g(indep)s(enden)m (t)e(of)i(ZF)o(,)i(no)d(matter)h(whic)m(h)0 430 y(T)-8 b(uring)30 b(mac)m(hine)h(is)f(used)g(to)h(sp)s(ecify)f Fn(O)s FD(?)141 543 y(The)k(answ)m(er)f(turns)g(out)h(b)s(e)f(y)m(es,)j (as)e(sho)m(wn)f(b)m(y)h(Hartmanis)g([25)q(])g(and)g(also)h(b)m(y)e (Kurtz,)i(O'Donnell,)h(and)0 656 y(Ro)m(y)m(er)31 b([33)q(].)70 b(Skipping)29 b(tec)m(hnicalities,)k(the)d(in)m(tuition)g(is)g(as)g (follo)m(ws.)71 b(W)-8 b(e)31 b(construct)f Fn(O)i FD(so)e(that)g(for)g (almost)0 769 y(all)h(input)f(lengths,)g Fn(O)j FD(collapses)f FC(P)e FD(and)g FC(NP)q FD(.)71 b(But)30 b(for)g(a)h(few,)f (widely-separated)h(input)f(lengths,)g(call)i(them)0 882 y Fp(f)24 b FD(\()q(1\))16 b Fp(;)f(f)25 b FD(\(2\))16 b Fp(;)f(f)25 b FD(\(3\))16 b Fp(;)f(:)g(:)g(:)r FD(,)27 b Fn(O)i FD(separates)e FC(P)f FD(and)g FC(NP)p FD(,)h(and)e(that)i(is) f(enough)g(to)h(guaran)m(tee)h(that)f FC(P)e Fn(6)p FD(=)g FC(NP)i FD(relativ)m(e)0 995 y(to)33 b Fn(O)s FD(,)h(since)f(there)g (are)g(in\014nitely)g(man)m(y)f(suc)m(h)h(lengths.)66 b(The)32 b(catc)m(h)i(no)m(w)f(is)g(that)g(the)g(function)f Fp(f)10 b FD(,)33 b(though)0 1108 y(computable,)26 b(gro)m(ws)f Fq(so)31 b FD(quic)m(kly)25 b(that)g(one)f(can't)h(pro)m(v)m(e)h(in)e (ZF)g(that)h Fp(f)33 b FD(is)25 b(total,)h(or)e(ev)m(en)h(that)g Fp(f)34 b FD(is)24 b(de\014ned)f(for)0 1220 y(in\014nitely)j(man)m(y)h (v)-5 b(alues)26 b(of)h Fp(n)p FD(.)65 b(\(W)-8 b(e'll)28 b(ha)m(v)m(e)g(more)e(to)h(sa)m(y)g(ab)s(out)f(suc)m(h)g(fast-gro)m (wing)i(computable)e(functions)0 1333 y(in)35 b(Section)g(5.\))90 b(If)35 b Fp(f)44 b FD(w)m(ere)35 b(de\014ned)f(for)h(only)g (\014nitely)g(man)m(y)g Fp(n)p FD(,)h(then)e Fn(O)k FD(w)m(ould)d (di\013er)f(only)h(\014nitely)g(from)0 1446 y(an)c(oracle)h(that)g (collapses)g FC(P)f FD(and)f FC(NP)q FD(,)h(so)g(of)g(course)g(w)m(e'd) g(ha)m(v)m(e)i FC(P)2382 1413 y Ff(O)2470 1446 y FD(=)26 b FC(NP)2689 1409 y Ff(O)2751 1446 y FD(.)73 b(That's)31 b(what)g(mak)m(es)h FC(P)3698 1413 y Ff(O)3791 1446 y FD(vs.)0 1559 y FC(NP)122 1522 y Ff(O)215 1559 y FD(indep)s(enden)m(t)d (of)h(ZF.)0 1803 y Fj(3.2)112 b(W)-9 b(eak)38 b(Indep)s(endence)0 1974 y FD(If)28 b(w)m(e)h(w)m(an)m(t)g(to)g(study)e(the)i(pro)m(v)-5 b(abilit)m(y)30 b(of)e FC(P)h FD(vs.)f FC(NP)q FD(,)g(a)h(natural)f (idea)h(is)g(to)g(sho)m(w)f(the)g(problem)g(indep)s(enden)m(t)0 2087 y(of)h(extremely)i Fq(we)-5 b(ak)39 b FD(logical)32 b(theories.)70 b(If)29 b(nothing)g(else,)i(that)e(w)m(ould)g(at)h (least)h(rule)e(out)g(an)m(y)h(approac)m(h)f(to)h FC(P)0 2200 y FD(vs.)j FC(NP)g FD(that)h(can)f(b)s(e)f(formalized)i(within)f (those)g(theories.)82 b(Already)33 b(in)g(the)g(sev)m(en)m(ties)i(and)d (early)i(eigh)m(ties,)0 2313 y(there)d(w)m(as)f(a)h(go)s(o)s(d)f(deal)h (of)g(w)m(ork)f(in)g(this)h(direction)g([15)q(,)f(28)q(,)h(58)q(];)g(w) m(e'll)g(lo)s(ok)g(at)g(t)m(w)m(o)h(examples.)141 2426 y(DeMillo)40 b(and)d(Lipton)g([15)q(])h(sho)m(w)f FC(P)g Fn(6)p FD(=)g FC(NP)h FD(unpro)m(v)-5 b(able)37 b(in)g(a)h(fragmen)m(t) g(of)f(n)m(um)m(b)s(er)f(theory)i(they)g(call)0 2539 y(ET.)67 b(The)27 b(ob)5 b(jects)28 b(of)g(ET)f(are)h(in)m(tegers,)h (while)f(the)g(language)g(consists)h(of)e(the)h(functions)f Fp(x)15 b FD(+)g Fp(y)s FD(,)26 b Fp(x)15 b Fn(\000)g Fp(y)s FD(,)27 b Fp(x)15 b Fn(\001)g Fp(y)s FD(,)0 2652 y(min)g Fn(f)p Fp(x;)g(y)s Fn(g)q FD(,)35 b(max)15 b Fn(f)q Fp(x;)g(y)s Fn(g)p FD(,)35 b(and)f Fp(c)1153 2619 y Fo(x)1231 2652 y FD(\(where)g Fp(c)g FD(is)g(a)h(constan)m(t\);)h(as) e(w)m(ell)h(as)f(all)h(p)s(olynomial-time)g(computable)0 2765 y Fq(pr)-5 b(e)g(dic)g(ates)43 b FD(\(but)33 b(not)h(functions\).) 82 b(F)-8 b(or)34 b(example,)h(giv)m(en)f(in)m(tegers)h Fp(x;)15 b(y)s(;)g(z)t FD(,)35 b(w)m(e)f(can)f(write)h(a)f(predicate)h (that)0 2877 y(tests)g(whether)e(2)612 2845 y Fo(x)679 2877 y FD(+)21 b(3)816 2845 y Fo(y)888 2877 y FD(=)30 b(5)1034 2845 y Fo(z)1074 2877 y FD(.)82 b(W)-8 b(e)34 b(can)g(do)f(this)g(ev)m(en)g(though)g Fn(j)p FD(2)2409 2845 y Fo(x)2454 2877 y Fn(j)22 b FD(+)g Fn(j)p FD(3)2664 2845 y Fo(y)2706 2877 y Fn(j)g FD(+)g Fn(j)p FD(5)2916 2845 y Fo(z)2956 2877 y Fn(j)34 b FD(is)f(exp)s(onen)m(tially)h(larger) 0 2990 y(than)29 b Fn(j)p Fp(x)p Fn(j)18 b FD(+)f Fn(j)p Fp(y)s Fn(j)h FD(+)f Fn(j)q Fp(z)t Fn(j)p FD(|since)29 b(it's)h(only)f(the)h(predicates)f(\(in)g(this)g(case)h(equalit)m(y)h (testing\),)g(not)e(the)h(arithmetic)0 3103 y(op)s(erations,)42 b(that)e(need)f(to)h(b)s(e)f(p)s(olynomial-time.)108 b(Finally)-8 b(,)44 b(the)39 b(axioms)h(of)g(ET)f(are)g(all)i(true)e (sen)m(tences)0 3216 y(of)k(the)f(form)g Fn(8)p Fp(x)g(A)15 b FD(\()q Fp(x)p FD(\),)43 b(where)f Fp(A)g FD(is)h(a)g(quan)m (ti\014er-free)g(predicate.)120 b(\(Here)43 b(`true')g(means)f(true)h (for)f(the)0 3329 y(ordinary)28 b(in)m(tegers.\))70 b(In)28 b(one)h(sense)f(the)h(axioms)g(are)g(absurdly)e(p)s(o)m(w)m (erful|among)i(other)g(things,)g(they)f(giv)m(e)0 3442 y(us)g(F)-8 b(ermat's)29 b(Last)g(Theorem)f(for)g(free)g(\(for)h(eac)m (h)g(\014xed)f(v)-5 b(alue)29 b(of)f Fp(n)p FD(\)|but)f(in)h(another)h (sense)f(the)h(axioms)g(are)0 3555 y(w)m(eak,)34 b(since)f(they)f(ha)m (v)m(e)i(only)e(one)h(univ)m(ersal)f(quan)m(ti\014er.)79 b(The)32 b(pro)s(of)f(that)i FC(P)28 b Fn(6)p FD(=)h FC(NP)j FD(is)h(unpro)m(v)-5 b(able)31 b(in)h(ET)0 3668 y(w)m(ould)f(tak)m(e)i(us)e(to)s(o)h(far)f(a\014eld.)75 b(I'll)31 b(just)g(sa)m(y)h(that)g(a)g(k)m(ey)g(part)f(is)g(to)h(b)s (ound)e(the)h(p)s(ossible)g(gro)m(wth)h(rates)g(of)0 3781 y(functions)e(expressible)g(with)g(the)h(allo)m(w)m(ed)h (arithmetic)g(op)s(erations.)2414 3748 y Fy(8)141 3894 y FD(Sazano)m(v)k([58)q(])f(sho)m(ws)g(exp)s(onen)m(tial)g(lo)m(w)m(er) h(b)s(ounds)d(to)i(b)s(e)f(unpro)m(v)-5 b(able)35 b(in)f(a)h(quite)g (di\013eren)m(t)g(theory)-8 b(,)37 b(b)m(y)0 4007 y(using)43 b(the)g(metho)s(d)g(of)g(consistency)h(strength)g(discussed)e(in)h (Section)h(2.2.)123 b(He)44 b(de\014nes)e(a)i(theory)f(T)g(in)0 4120 y(whic)m(h)32 b(the)h(ob)5 b(jects)33 b(are)g(\014nite)f(binary)f (strings,)i(and)f(w)m(e)h(ha)m(v)m(e)h(a)m(v)-5 b(ailable)34 b(all)g(p)s(olynomial-time)f(computable)0 4232 y(functions)39 b(and)g(predicates.)109 b(Call)40 b(a)g(sen)m(tence)h(`true')f(if)g (it's)g(true)f(in)h(the)f(standard)g(mo)s(del.)108 b(Then)39 b(the)0 4345 y(axioms)d(consist)g(of)g(all)g(true)g(\014rst-order)e (sen)m(tences,)k(with)d(all)i(quan)m(ti\014ers)g Fq(b)-5 b(ounde)g(d)46 b FD(\(except)37 b(for)e(an)h(initial)0 4458 y(univ)m(ersal)k(quan)m(ti\014er\).)111 b(A)40 b(b)s(ounded)e (quan)m(ti\014er)i(has)g(the)h(form)e Fn(8)p Fp(x)i Fn(\024)h Fp(a)e FD(or)g Fn(9)p Fp(x)h Fn(\024)g Fp(a)p FD(,)i(where)d Fp(a)g FD(do)s(esn't)0 4571 y(dep)s(end)27 b(on)i Fp(x)g FD(and)g Fn(\024)f FD(denotes)i(lexicographic)h(ordering)e(of)g (strings.)69 b(This)28 b(is)h(a)h(ric)m(her)f(axiom)h(set)g(than)e (that)0 4684 y(considered)e(b)m(y)f(DeMillo)j(and)e(Lipton;)h(on)f(the) g(other)g(hand,)g(the)g(arithmetic)h(op)s(erations|and)e(in)h (particular)0 4797 y(the)31 b(exp)s(onen)m(tial)g(function|aren't)f(a)m (v)-5 b(ailable.)p 0 4876 1560 4 v 104 4930 a Fu(8)138 4962 y Ft(As)21 b(a)h(further)f(result,)h(DeMillo)h(and)e(Lipton)g(sho) n(w)g(that)g(assuming)h Fs(P)g Fe(6)p Ft(=)f Fs(NP)p Ft(,)i(the)d(statemen)n(t)i Fs(NP)f Fe(6)p Ft(=)g Fs(coNP)h Ft(is)g(consisten)n(t)g(with)0 5053 y(another)i(fragmen)n(t)h(of)g(n)n (um)n(b)r(er)e(theory)h(called)h(PT)q(.)48 b(This)25 b(represen)n(ts)f(a)g(direction)h(on)f(whic)n(h)g(there)g(hasn't)g(b)r (een)g(m)n(uc)n(h)f(w)n(ork)i(to)0 5144 y(m)n(y)i(kno)n(wledge:)38 b(pro)n(viding)28 b(\\evidence")g(for)g(widely-b)r(eliev)n(ed)f (complexit)n(y)g(assumptions)i(\(suc)n(h)d(as)i Fs(NP)d Fe(6)p Ft(=)f Fs(coNP)q Ft(,)k(or)g Fs(P)c Fe(6)p Ft(=)g Fs(NP)q Ft(\),)0 5236 y(b)n(y)i(sho)n(wing)i(that)f(the)g(assumptions)h (are)f Fl(c)l(onsistent)37 b Ft(with)27 b(w)n(eak)g(logical)j(theories) e(\(or)f(equiv)l(alen)n(tly)-6 b(,)26 b(that)h(their)g(negations)h(are) 0 5327 y(unpro)n(v)l(able)d(in)g(those)h(theories\).)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 141 91 a FD(Giv)m(en)26 b(strings)g Fp(x)f FD(and)g Fp(y)s FD(,)h(w)m(e)g(can)g(de\014ne)e(a)i(predicate)g (EXP)15 b(\()q Fp(x;)g(y)s FD(\),)27 b(that)f(tests)g(whether)f(2)3304 58 y Ff(j)p Fo(x)p Ff(j)3412 91 y Fn(\024)g(j)q Fp(y)s Fn(j)g FD(\(where)0 204 y Fn(j)p Fp(x)p Fn(j)39 b FD(is)g(the)f(length) h(of)g Fp(x)p FD(\).)104 b(Ho)m(w)m(ev)m(er,)43 b(w)m(e)c(don't)f(ha)m (v)m(e)i(an)e(axiom)i(E)e(sa)m(ying)i(that)f Fn(8)p Fp(x)p Fn(9)p Fp(y)h FD(EXP)15 b(\()p Fp(x;)g(y)s FD(\))q(.)104 b(In)0 317 y(other)32 b(w)m(ords,)f(if)g(our)g(quan)m(ti\014ers)g (range)h(o)m(v)m(er)h(strings)e(of)g(length)h Fp(n)p FD(,)g(then)f(strings)g(of)g(length)h(2)3385 284 y Fo(n)3464 317 y FD(are)g(outside)0 430 y(our)k(\\univ)m(erse)i(of)f(discourse.") 74 b(Indeed)36 b(Sazano)m(v)j(sho)m(ws)d(that)i(T)15 b(+)g(E)36 b Fh(\017)f FD(Con)15 b(\()q(T)o(\))q(.)97 b(In)m(tuitiv)m(ely)-8 b(,)41 b(once)c(w)m(e)0 543 y(ha)m(v)m(e)h(an)f (exp)s(onen)m(tially-long)j(string)d Fp(y)s FD(,)h(w)m(e)g(can)f (construct)h(the)f(set)h(of)f Fq(al)5 b(l)47 b FD(p)s(olynomial-size)39 b(strings,)g(and)0 656 y(thereb)m(y)44 b(obtain)g(a)g(mo)s(del)g(for)f (T.)124 b(This)43 b(is)h(analogous)h(to)g(the)f(fact)g(that)h(ZF)i Fh(\017)g FD(Con)15 b(\(P)-8 b(A)q(\)|the)44 b(only)0 769 y(di\013erence)d(b)s(eing)f(that)g(in)g(Sazano)m(v's)i(case,)i(the) c(Axiom)h(of)f(In\014nit)m(y)g(is)g(scaled)h(do)m(wn)f(to)h(the)g (\\Axiom)g(of)0 882 y(Exp)s(onen)m(tialit)m(y")d(E.)93 b(Con)m(tin)m(uing)37 b(the)f(analogy)-8 b(,)40 b(w)m(e)c(can)g (conclude)h(that)g(T)d Fn(6)p Fh(\017)g FD(E|since)i(otherwise)h(w)m (e'd)0 995 y(ha)m(v)m(e)g(T)c Fh(\017)g FD(Con)15 b(\(T\),)37 b(con)m(tradicting)h(the)d(Incompleteness)h(Theorem.)91 b(Indeed,)36 b(letting)h(A)m(CCEPT)e(b)s(e)g(the)0 1108 y(assertion)g(that)g(there)g(exists)g(an)f(algorithm)i(for)e(SA)-8 b(T,)35 b(Sazano)m(v)h(sho)m(ws)e(further)f(that)i(T)15 b(+)g(A)m(CCEPT)31 b Fn(6)p Fh(\017)h FD(E.)0 1220 y(No)m(w)39 b(let)g(ELB)f(\(Exp)s(onen)m(tial)g(Lo)m(w)m(er)h(Bound\))f(b)s(e)f (the)h(assertion)h(that)g(an)m(y)f(algorithm)h(for)f(SA)-8 b(T)37 b(requires)0 1333 y(exp)s(onen)m(tial)31 b(time.)72 b(Then)1427 1446 y(T)15 b(+)g(A)m(CCEPT)f(+)h(ELB)26 b Fh(\017)e FD(E)15 b Fp(:)0 1613 y FD(F)-8 b(or)46 b(A)m(CCEPT)f (tells)h(us)f(that)h(for)f(all)i(SA)-8 b(T)45 b(instances)h Fp(x)p FD(,)j(there)d(exists)g(a)f Fp(y)k FD(that)d(is)f(the)h(tableau) g(of)g(a)0 1726 y(computation)27 b(of)g(SA)-8 b(T)15 b(\()p Fp(x)p FD(\))27 b(b)m(y)f(some)h(\014xed)f(algorithm.)66 b(Mean)m(while)28 b(ELB)e(tells)i(us)e(that)h Fn(j)p Fp(y)s Fn(j)f FD(is)h(exp)s(onen)m(tially)0 1839 y(larger)c(than)f Fn(j)q Fp(x)p Fn(j)g FD(in\014nitely)h(often.)61 b(W)-8 b(e)23 b(conclude)g(that)g(T)i Fn(6)p Fh(\017)g FD(ELB;)g(that)e(is,)i (T)d(is)g(unable)g(to)i(pro)m(v)m(e)f(exp)s(onen)m(tial)0 1952 y(lo)m(w)m(er)31 b(b)s(ounds)c(for)i(SA)-8 b(T)o(.)70 b(It's)30 b(in)m(teresting)g(that)g(this)f(pro)s(of)g(rules)g(out)g (only)h(lo)m(w)m(er)g(b)s(ounds)d(of)j(the)f(form)g(2)3819 1919 y Fo(n)3862 1895 y Fg(")0 2065 y FD(for)35 b Fp(")f(>)f FD(0,)j(since)f(w)m(e)h(need)f(an)g(exp)s(onen)m(tially)i(long)e (string)h(to)g(get)g(a)g(mo)s(del)f(for)g(T)o(.)91 b(F)-8 b(or)36 b(all)g(w)m(e)g(kno)m(w,)g(T)0 2178 y Fq(do)-5 b(es)39 b FD(pro)m(v)m(e)31 b(that)g(SA)-8 b(T)30 b(requires)g Fp(n)1251 2145 y Fy(log)13 b Fo(n)1431 2178 y FD(time.)141 2291 y(All)31 b(in)f(all,)h(w)m(e)g(depart)e(these)i(early)g(results)f (feeling)h(w)m(e)f(learned)h(a)f(bit)g(ab)s(out)g(logic,)i(indep)s (endence,)e(and)0 2403 y(relativization,)k(but)29 b(less)i(sure)f(that) h(w)m(e)f(learned)h(an)m(ything)g(ab)s(out)f FC(P)g FD(vs.)g FC(NP)q FD(.)0 2690 y FE(4)135 b(Natural)46 b(Pro)t(ofs)0 2893 y FD(In)39 b(1993,)45 b(Razb)s(oro)m(v)c(and)f(Rudic)m(h)f([56)r (])h(wrote)h(a)f(pap)s(er)f(that)i(con)m(tains,)j(arguably)-8 b(,)44 b(the)c(most)h(imp)s(ortan)m(t)0 3006 y(insigh)m(t)32 b(an)m(y)m(one)h(has)f(th)m(us)f(far)g(had)h(in)m(to)g(the)g FC(P)g FD(vs.)g FC(NP)g FD(question.)76 b(Lo)s(osely)33 b(sp)s(eaking,)f(they)g(said)f(that)i(the)0 3119 y(reason)h FC(P)e Fn(6)p FD(=)f FC(NP)j FD(is)g(so)g(di\016cult)g(to)h(pro)m(v)m (e)g(is)f(that)h FC(P)c Fn(6)p FD(=)g FC(NP)q FD(!)2181 3086 y Fy(9)2306 3119 y FD(I'll)j(\014rst)f(review)i(their)f(argumen)m (t;)i(then,)f(in)0 3232 y(Section)j(4.1,)j(I'll)d(discuss)f(ho)m(w)g (it)h(can)g(b)s(e)f(used)g(to)h(sho)m(w)g(the)f(unpro)m(v)-5 b(abilit)m(y)38 b(of)g(circuit)g(lo)m(w)m(er)h(b)s(ounds)c(in)0 3344 y(certain)c(logical)i(theories.)141 3457 y(As)41 b(men)m(tioned)g(in)g(Section)h(1,)i(in)c(the)h(1980's)i(p)s(eople)e (dev)m(elop)s(ed)g(man)m(y)g(`com)m(binatorial')i(tec)m(hniques)0 3570 y(for)g(pro)m(ving)h(circuit)g(lo)m(w)m(er)h(b)s(ounds)c([2)q(,)j (18)q(,)f(52)q(,)h(61)q(].)124 b(These)43 b(tec)m(hniques)h(sho)m(w)m (ed,)j(for)d(example,)j(that)0 3683 y(the)30 b(P)-8 b(ARITY)32 b(function)d(requires)h(constan)m(t-depth)g(circuits)h(of)f(exp)s(onen) m(tial)g(size,)h(pro)m(vided)f(the)g(only)f(gates)0 3796 y(allo)m(w)m(ed)36 b(are)f Fn(_)p Fp(;)15 b Fn(^)p Fp(;)g Fh(q)34 b FD(\(with)g(un)m(b)s(ounded)e(fanin\).)86 b(What)34 b(Razb)s(oro)m(v)h(and)f(Rudic)m(h)f(noticed)i(w)m(as)g(that)f(these)0 3909 y(tec)m(hniques)27 b(all)g(follo)m(w)g(the)g(same)f(basic)h (strategy)-8 b(.)67 b(T)-8 b(o)26 b(sho)m(w)g(that)h(a)g(Bo)s(olean)g (function)f Fp(f)35 b FD(:)25 b Fn(f)q FD(0)p Fp(;)15 b FD(1)p Fn(g)3489 3867 y Fo(n)3562 3909 y Fn(!)25 b(f)p FD(0)p Fp(;)15 b FD(1)p Fn(g)0 4022 y FD(\(sa)m(y)-8 b(,)32 b(P)-8 b(ARITY)r(\))31 b(is)g(not)f(in)g(complexit)m(y)i(class)f Fn(C)5 b FD(,)31 b(w)m(e)g(do)f(the)h(follo)m(wing.)66 4234 y(\(1\))46 b(In)m(v)m(en)m(t)22 b(a)g(`complexit)m(y)h(measure')p Fp(\026)f FD(for)f(Bo)s(olean)h(functions.)59 b(\(In)20 b([61)r(],)j(for)e(example,)j Fp(\026)d FD(is)g(the)h(minim)m(um)227 4347 y(degree)31 b(of)g(an)f(appro)m(ximating)h(p)s(olynomial)g(o)m(v)m (er)h(a)f(\014nite)f(\014eld.\))66 4535 y(\(2\))46 b(Sho)m(w)32 b(that)g(for)f(an)m(y)i(function)e Fp(f)1393 4502 y Ff(\003)1459 4535 y Fn(2)d(C)5 b FD(,)32 b Fp(\026)15 b FD(\()p Fp(f)1818 4502 y Ff(\003)1857 4535 y FD(\))32 b(is)g(small.)77 b(\(Sa)m(y)-8 b(,)33 b(b)s(ecause)f(eac)m(h)h(gate)h(in)d(a)h(circuit)h (can)227 4648 y(only)e(increase)g Fp(\026)f FD(b)m(y)g(a)h(small)g (amoun)m(t.\))66 4836 y(\(3\))46 b(Sho)m(w)30 b(that)h Fp(\026)15 b FD(\()p Fp(f)10 b FD(\))30 b(is)h(large|from)g(whic)m(h)f (it)h(follo)m(ws)g(that)g Fp(f)45 b(=)-55 b Fn(2)25 b(C)5 b FD(.)p 0 4920 1560 4 v 104 4974 a Fu(9)138 5005 y Ft(Of)29 b(course,)h(assuming)g Fs(P)c Fe(6)p Ft(=)g Fs(NP)p Ft(,)k(one)f(could) f(cite)h(that)g(as)g(the)f(reason)i(wh)n(y)e Fl(anything)36 b Ft(is)29 b(hard)f(to)h(pro)n(v)n(e!)71 b(But)29 b(Razb)r(oro)n(v)0 5097 y(and)e(Rudic)n(h)f(connected)h(the)g(hardness)g(of)h Fs(NP)f Ft(problems)h(to)f(the)g(hardness)h(of)g(pro)n(ving)f(their)g (hardness)g(in)g(a)h(more)f(in)n(teresting)0 5188 y(w)n(a)n(y)-6 b(.)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 141 91 a FD(The)36 b(p)s(oin)m(t)f(is)h(that,)j (if)c(the)h(strategy)i(ab)s(o)m(v)m(e)f(w)m(orks,)g(then)f(it)g(should) f(w)m(ork)h(not)g(only)g(for)g(the)g(function)0 204 y Fp(f)44 b FD(w)m(e're)35 b(in)m(terested)g(in,)h(but)e(for)g(man)m(y)g (other)h(functions)f(as)h(w)m(ell.)88 b(F)-8 b(or)35 b(under)e(an)m(y)i(`reasonable')h(measure)0 317 y(of)i(complexit)m(y)-8 b(,)42 b(a)d(random)e(function)h(is)g(extremely)h(complex.)102 b(In)m(tuitiv)m(ely)-8 b(,)42 b(if)c(`simple')g(means)g(ha)m(ving)h(a)0 430 y(short)31 b(description)h(of)g(some)g(form,)g(then)f(most)h (functions)f(can't)i(b)s(e)e(simple)g(just)g(b)m(y)h(a)g(coun)m(ting)g (argumen)m(t!)0 543 y(Indeed,)24 b(this)g(is)f(ho)m(w)h(one)g(sho)m(ws) f(that)h(almost)h(all)f(Bo)s(olean)h(functions)e(ha)m(v)m(e)i(exp)s (onen)m(tial)f(circuit)h(complexit)m(y)-8 b(,)0 656 y(and)33 b(that)i(almost)g(all)g(strings)f(ha)m(v)m(e)h(large)h(Kolmogoro)m(v)g (complexit)m(y)-8 b(.)88 b(F)-8 b(urthermore,)35 b(assuming)e(w)m(e)i (could)0 769 y(analyze)44 b Fp(\026)15 b FD(\()q Fp(f)10 b FD(\))42 b(w)m(ell)i(enough)e(to)i(carry)f(out)g(step)g(\(3\),)k(w)m (e)c(presumably)f(ha)m(v)m(e)i(an)f Fq(e\016cient)h(pr)-5 b(o)g(c)g(e)g(dur)g(e)52 b FD(to)0 882 y(estimate)32 b Fp(\026)p FD(|where)e(`e\016cien)m(t')i(means)e(using)g(time)h(p)s (olynomial)g(in)f(2)2503 849 y Fo(n)2550 882 y FD(,)h(the)g(size)g(of)f (the)h(truth-table)g(of)f Fp(f)10 b FD(.)141 995 y(Assuming)30 b(our)g(pro)s(of)g(is)g(`natural')h(in)f(the)h(ab)s(o)m(v)m(e)h (senses,)e(Razb)s(oro)m(v)i(and)d(Rudic)m(h)h(sho)m(w)h(that)g(w)m(e)g (could)0 1108 y(turn)i(the)i(pro)s(of)f(on)g(its)h(head,)h(and)e(use)g (it)h(to)g(break)g(pseudorandom)e(functions)h(computable)h(b)m(y)f(the) h(class)0 1220 y Fn(C)5 b FD(.)102 b(The)38 b(idea)h(is)f(simple:)56 b(if)38 b Fp(f)1154 1187 y Ff(\003)1231 1220 y Fn(2)g(C)5 b FD(,)41 b(then)c Fp(\026)15 b FD(\()q Fp(f)1824 1187 y Ff(\003)1863 1220 y FD(\))38 b(m)m(ust)g(b)s(e)g(small,)i(while)f(if) f Fp(f)47 b FD(is)38 b(a)h(gen)m(uinely)g(random)0 1333 y(function,)c(then)f Fp(\026)15 b FD(\()p Fp(f)10 b FD(\))34 b(is)g(large)i(with)e(non-negligible)h(probabilit)m(y)-8 b(.)88 b(A)34 b(subtlet)m(y)h(is)f(that)h(the)f(pro)s(cedure)f(to)0 1446 y(estimate)k Fp(\026)f FD(to)s(ok)g(time)h(p)s(olynomial)f(in)f(2) 1516 1413 y Fo(n)1563 1446 y FD(,)h(not)g(in)f Fp(n)p FD(.)92 b(T)-8 b(o)36 b(deal)g(with)g(this,)h(w)m(e)f(c)m(ho)s(ose)h (the)f(seed)f(for)h(the)0 1559 y(pseudorandom)26 b(function)i Fp(f)1013 1526 y Ff(\003)1077 1559 y Fn(2)c(C)33 b FD(to)c(ha)m(v)m(e)g (length)f Fp(n)1889 1526 y Fo(c)1923 1559 y FD(,)g(where)f Fp(c)h FD(is)g(a)g(large)h(constan)m(t.)69 b(Then)26 b(distinguishing)0 1672 y Fp(f)55 1639 y Ff(\003)129 1672 y FD(from)34 b(random)g(b)m(y)h(testing)h(ev)m(ery)g(seed)f (exhaustiv)m(ely)h(w)m(ould)f(tak)m(e)h(time)g(roughly)f(2)3156 1639 y Fo(n)3199 1616 y Fg(c)3235 1672 y FD(.)89 b(W)-8 b(e)37 b(succeeded)0 1785 y(instead)31 b(in)f(time)h(2)672 1752 y Fo(O)r Fy(\()p Fo(n)p Fy(\))830 1785 y FD(,)f(or)h(2)1042 1752 y Fo(N)1105 1729 y Fu(1)p Fg(=c)1234 1785 y FD(in)f(terms)g(of)h (the)f(seed)h(length)f Fp(N)36 b FD(=)25 b Fp(n)2588 1752 y Fo(c)2622 1785 y FD(.)141 1898 y(Wh)m(y)36 b(is)f(this)g (considered)g(implausible?)90 b(In)35 b(the)g(case)i Fn(C)h FD(=)33 b FC(P)p Fp(=)p FC(p)s(oly)k FD(\(that)f(is,)h(the)e(lo) m(w)m(er)i(b)s(ound)c(pro)s(of)0 2011 y(w)m(orks)h(against)h(p)s (olynomial-size)g(circuits\),)h(the)e(evidence)g(comes)h(cryptographic) f(reductions.)84 b(H)-11 b(\027)-57 b(astad)34 b(et)0 2124 y(al.)39 b([27)r(])24 b(sho)m(w)m(ed)h(that)h(giv)m(en)f(an)m(y)g (one-w)m(a)m(y)h(function,)g(w)m(e)f(can)g(construct)g(a)g (pseudorandom)e(generator)j(that's)0 2237 y(roughly)34 b(as)h(hard)e(to)i(break.)87 b(Earlier,)36 b(Goldreic)m(h,)h(Goldw)m (asser,)f(and)e(Micali)i([21)q(])f(had)e(sho)m(wn)h(that)h(giv)m(en)0 2350 y(an)m(y)27 b(pseudorandom)e(generator,)j(w)m(e)g(can)f(construct) g(a)g(pseudorandom)e Fq(function)34 b FD(that's)27 b(roughly)g(as)f (hard)g(to)0 2462 y(break.)79 b(Putting)33 b(these)g(together,)i(w)m(e) e(\014nd)e(that)i(our)f(lo)m(w)m(er)h(b)s(ound)e(pro)s(of)h(w)m(ould)g (giv)m(e)i(us)e(a)g(w)m(a)m(y)i(to)f(break)0 2575 y(an)m(y)h(one-w)m(a) m(y)h(function)e(\(including)h(factoring,)i(discrete)e(logarithm,)h (etc.\),)i(in)c(time)h(2)3113 2542 y Fo(O)r Fy(\()q Fo(n)3240 2519 y Fg(")3273 2542 y Fy(\))3338 2575 y FD(for)f(an)m(y)h Fp(")d(>)f FD(0.)0 2700 y(By)c(comparison,)h(the)f(b)s(est)f(kno)m(wn)g (factoring)h(algorithm)h(is)f(conjectured)f(to)i(run)d(in)h(time)h (roughly)g(2)3564 2667 y Fo(n)3607 2644 y Fu(1)p Fg(=)p Fu(3)3733 2700 y FD([35)q(].)141 2813 y(If)35 b Fn(C)41 b FD(is)35 b(a)h(smaller)g(class,)i(for)d(instance)i(the)e(class)i FC(TC)2071 2776 y Fy(0)2145 2813 y FD(of)f(constan)m(t-depth)g(p)s (olynomial-size)i(threshold)0 2926 y(circuits,)f(then)f(the)g (reductions)g(of)g([27)q(])g(and)g([21)q(])g(can't)h(b)s(e)e(carried)i (out.)93 b(Ho)m(w)m(ev)m(er,)40 b(Naor)d(and)e(Reingold)0 3039 y([40)q(])h(ga)m(v)m(e)h(a)e(direct)h(construction)g(of)f(a)h (pseudorandom)d(function)i(in)g FC(TC)2647 3002 y Fy(0)2686 3039 y FD(,)i(whic)m(h)e(is)g(pro)m(v)-5 b(ably)35 b(as)h(hard)e(as)0 3152 y(factoring)k(and)d(discrete)j(logarithm.)96 b(It)36 b(follo)m(ws)i(that)f(an)m(y)g(natural)f(pro)s(of)g(that)h(a)g (function)f(isn't)g(in)h FC(TC)3861 3115 y Fy(0)0 3265 y FD(w)m(ould)30 b(yield)h(an)f(algorithm)i(for)e(these)g(problems)g(m) m(uc)m(h)h(faster)f(than)g(an)m(y)h(kno)m(wn)f(to)s(da)m(y)-8 b(.)141 3378 y(A)28 b(\014nal)f(observ)-5 b(ation)28 b(is)f(that)h(the)g(stronger)g(the)f(lo)m(w)m(er)i(b)s(ound)c(w)m(e)j (obtain)g(for)f Fp(f)10 b FD(,)28 b(the)g(stronger)f(the)h Fq(upp)-5 b(er)0 3491 y FD(b)s(ound)38 b(it)k(implies)e(for)h(breaking) f(pseudorandom)f(functions.)112 b(F)-8 b(or)41 b(example,)j(if)c(our)g (lo)m(w)m(er)i(b)s(ound)d(puts)0 3603 y Fp(f)46 b FD(outside)38 b(of)f Fn(C)42 b FD(=)36 b FC(DTIME)15 b FD(\()p Fp(t)g FD(\()p Fp(n)p FD(\)\))38 b(\(where)f Fp(t)f FD(is)i(sup)s(erp)s (olynomial\),)g(then)f(w)m(e)g(can)h(tak)m(e)g(the)g(seed)f(for)g(the)0 3716 y(pseudorandom)23 b(function)h(to)i(ha)m(v)m(e)g(length)f(ab)s (out)f Fp(t)15 b FD(\()p Fp(n)p FD(\).)63 b(So)25 b(in)f(terms)h(of)f (the)h(seed)g(length,)h(w)m(e)f(get)h(a)f(roughly)0 3829 y(2)45 3796 y Fo(t)70 3773 y Fd(\000)p Fu(1)153 3796 y Fy(\()q Fo(n)p Fy(\))287 3829 y FD(upp)s(er)30 b(b)s(ound)g(on)i(the) g(time)h(needed)f(to)g(distinguish)g(the)g(function)g(from)f(random.)77 b(Razb)s(oro)m(v)33 b(and)0 3942 y(Rudic)m(h)j(credit)h(Wigderson)g (with)f(the)h(am)m(using)g(observ)-5 b(ation)37 b(that)h(no)e(natural)h (pro)s(of)f(can)g(sho)m(w)h(a)g(b)s(etter)0 4055 y(than)d(half-exp)s (onen)m(tial)851 4022 y Fy(10)961 4055 y FD(lo)m(w)m(er)i(b)s(ound)c (for)i(the)h(discrete)g(logarithm)g(function,)g Fq(unc)-5 b(onditional)5 b(ly)p FD(.)90 b(F)-8 b(or)35 b(as)0 4168 y(w)m(e)c(sho)m(w)f(this)g(function)g(to)i(b)s(e)d(harder,)h(w)m(e)h (sim)m(ultaneously)g(sho)m(w)f(it)h(to)g(b)s(e)f(easier!)0 4411 y Fj(4.1)112 b(Natural)38 b(Pro)s(ofs)f(and)i(Indep)s(endence)0 4583 y FD(In)27 b(Section)h(3.2,)h(w)m(e)f(sa)m(w)f(what)h(migh)m(t)g (b)s(e)e(called)j(the)e(`\014rst)g(generation')i(of)e FC(P)h FD(vs.)f FC(NP)h FD(indep)s(endence)e(results.)0 4696 y(These)k(sough)m(t)h(to)h(sho)m(w)e FC(P)c Fn(6)p FD(=)f FC(NP)31 b FD(unpro)m(v)-5 b(able)30 b(in)g(w)m(eak)i(logical)h (theories,)e(b)m(y)g(\(sa)m(y\))h(analyzing)g(the)e(p)s(ossible)0 4809 y(gro)m(wth)i(rates)g(of)g(functions)f(pro)m(v)-5 b(ably)32 b(total)h(in)e(those)h(theories.)77 b(Razb)s(oro)m(v)32 b(and)f(Rudic)m(h)g(op)s(ened)g(the)h(w)m(a)m(y)0 4922 y(to)f(a)g(`second)g(generation')h(of)e(indep)s(endence)f(results.)71 b(These)30 b(fo)s(cus)g(on)g(a)h(\014nite)f(statemen)m(t,)j(suc)m(h)d (as)p 0 5001 1560 4 v 73 5055 a Fu(10)138 5086 y Ft(F)-6 b(or)34 b Fr(t)12 b Ft(\()p Fr(n)p Ft(\))34 b(to)g(b)r(e)f(half-exp)r (onen)n(tial)h(means)g(that)f Fr(t)13 b Ft(\()p Fr(t)f Ft(\()p Fr(n)p Ft(\)\))33 b(gro)n(ws)i(lik)n(e)f(2)2357 5055 y Fg(n)2400 5086 y Ft(.)91 b(Suc)n(h)33 b(functions)h(exist,)i (but)c(are)i(di\016cult)g(to)0 5178 y(describ)r(e)26 b(\(see)g(Miltersen,)h(Vino)r(dc)n(handran,)f(and)f(W)-6 b(atanab)r(e)26 b([37)q(]\).)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 911 204 a Fh(q)15 b FD(Circuit)1249 218 y Fo(n)1322 204 y FD(:=)55 b(\\)16 b(SA)-8 b(T)1710 218 y Fo(n)1803 204 y FD(requires)30 b(circuits)h(of)f(size)h Fp(n)2794 167 y Fy(log)13 b Fo(n)2944 204 y FD(")0 371 y(where)26 b(SA)-8 b(T)435 385 y Fo(n)508 371 y FD(is)27 b(the)f(set)g(of)h(SA)-8 b(T)26 b(instances)g(of)g(size)h Fp(n)p FD(.)65 b(The)26 b(goal)h(is)g(to)f(sho)m(w)g(\(p)s(erhaps)f (under)g(a)h(complexit)m(y)0 484 y(assumption\))40 b(that)g(in)f(some)i (pro)s(of)e(system,)j Fh(q)15 b FD(Circuit)2009 498 y Fo(n)2095 484 y FD(requires)40 b(pro)s(ofs)f(of)h(length)g(sup)s(erp)s (olynomial)e(in)0 597 y Fp(n)p FD(.)76 b(That)31 b(is,)i(w)m(e)f(w)m (an)m(t)g(to)h(argue)f(against)h(the)f(plausibilit)m(y)g(of)g(pro)m (ving)g(lo)m(w)m(er)h(b)s(ounds)c(b)m(y)j(pro)m(ving)g(a)g(lo)m(w)m(er) 0 710 y(b)s(ound.)141 823 y(The)27 b(di\013erence)h(b)s(et)m(w)m(een)g (the)f(t)m(w)m(o)i(generations)f(of)g(indep)s(endence)e(result)h (highligh)m(ts)h(an)g(imp)s(ortan)m(t)f(fact)0 936 y(ab)s(out)d FC(P)h FD(vs.)f FC(NP)h FD(itself.)64 b(When)24 b(w)m(e)h(meet)g(a)g (statemen)m(t|Goldbac)m(h's)j(Conjecture,)d(for)g(example|that)g(sa)m (ys)0 1049 y(something)32 b(ab)s(out)f(ev)m(ery)i(natural)e(n)m(um)m(b) s(er)f Fp(n)p FD(,)i(w)m(e)g(usually)f(assume)h(the)f(statemen)m(t)j (is)d(trivial)i(for)e(an)m(y)h Fq(\014xe)-5 b(d)0 1161 y Fp(n)p FD(.)63 b(So)25 b(the)g(sole)h(problem)f(is)g(to)g(\014nd)f (an)h(argumen)m(t)g(that)h(w)m(orks)f(for)f(all)i Fp(n)p FD(.)64 b(F)-8 b(or)25 b Fh(q)15 b FD(Circuit)3165 1175 y Fo(n)3212 1161 y FD(,)26 b(though,)g(w)m(e)g(ha)m(v)m(e)0 1274 y(no)37 b(idea)g(ho)m(w)f(to)i(pro)m(v)m(e)f(ev)m(en)h Fh(q)15 b FD(Circuit)1447 1288 y Fy(50)1559 1274 y FD(or)36 b Fh(q)15 b FD(Circuit)2015 1288 y Fy(100)2125 1274 y FD(.)96 b(The)36 b(resources)h(needed)f(to)i(pro)m(v)m(e)f Fh(q)15 b FD(Circuit)3853 1288 y Fo(n)0 1387 y FD(gro)m(w)30 b(to)s(o)g(quic)m(kly)h(as)e(a)h(function)g(of)f Fp(n)p FD(.)70 b(Both)30 b(natural)g(pro)s(ofs)e(and)h(the)h (second-generation)h(indep)s(endence)0 1500 y(results)26 b(fo)s(cus)h(exclusiv)m(ely)h(on)e(this)h(latter)h(`meta-complexit)m (y')i(problem|b)m(ypassing)c(the)h(issue)f(of)h(ho)m(w)g(w)m(e'd)0 1613 y(generalize)32 b(to)g(all)f Fp(n)p FD(,)f(ev)m(en)h(if)f(w)m(e)h Fq(c)-5 b(ould)41 b FD(pro)m(v)m(e)31 b Fh(q)15 b FD(Circuit)2017 1627 y Fy(50)2092 1613 y FD(,)30 b Fh(q)15 b FD(Circuit)2486 1627 y Fy(100)2596 1613 y FD(,)30 b(and)g(so)h(on.)3061 1580 y Fy(11)141 1726 y FD(T)-8 b(o)36 b(do)g(justice)g(to)g(the)g (second-generation)h(indep)s(endence)e(results)g(w)m(ould)h(require)f (another)h(surv)m(ey)f(al-)0 1839 y(together,)h(and)d(indeed)g(suc)m(h) g(surv)m(eys)g(exist)h([10)q(,)g(46)q(,)f(49)q(].)83 b(Here)34 b(I'll)g(just)f(sk)m(etc)m(h)i(the)e(main)h(ideas.)83 b(Man)m(y)0 1952 y(of)32 b(the)g(results)g(in)m(v)m(olv)m(e)i(a)e(set)h (of)f(theories)h(called)g Fq(b)-5 b(ounde)g(d)35 b(arithmetic)k FD([9)q(,)32 b(10)q(,)g(11)q(].)64 b(In)31 b(these)h(theories,)i(the)0 2065 y(ob)5 b(jects)39 b(are)f(natural)g(n)m(um)m(b)s(ers,)h(and)e(w)m (e)i(ha)m(v)m(e)g(a)m(v)-5 b(ailable)40 b(the)f(constan)m(ts)g(0)f(and) g(1)g(and)f(the)h(functions)g(+,)0 2178 y Fn(\002)p FD(,)e Fn(\024)p FD(,)f Fn(b)q Fp(x=)p FD(2)p Fn(c)q FD(,)h Fn(j)p Fp(x)p Fn(j)q FD(,)g(and)e(#,)h(where)g Fn(j)p Fp(x)p Fn(j)e FD(=)f Fn(d)p FD(log)1693 2199 y Fy(2)1747 2178 y FD(\()q Fp(x)20 b FD(+)g(1\))q Fn(e)35 b FD(and)f Fp(x)p FD(#)p Fp(y)h FD(=)d(2)2639 2145 y Ff(j)p Fo(x)p Ff(j)o(\001j)p Fo(y)r Ff(j)2819 2178 y FD(.)88 b(W)-8 b(e)36 b(can)f(use)f(the)h Fq(b)-5 b(ounde)g(d)0 2291 y(quanti\014ers)40 b Fn(8)p Fp(x)26 b Fn(\024)h Fp(t)k FD(and)g Fn(9)p Fp(x)c Fn(\024)f Fp(t)p FD(,)32 b(where)f Fp(t)g FD(do)s(esn't)h(dep)s(end)d(on)j Fp(x)p FD(.)75 b(There)31 b(are)h(standard)f(axioms)h(de\014ning)0 2403 y(the)f(functions,)f(as)g(w)m(ell)i(as)e(t)m(w)m(o)i(t)m(yp)s(es)e(of)h (induction)f(axiom:)945 2608 y(IND)c(:)f([)q Fp(A)15 b FD(\(0\))21 b Fn(^)f(8)p Fp(x)15 b FD(\()p Fp(A)g FD(\()q Fp(x)p FD(\))25 b(=)-15 b Fn(\))25 b Fp(A)15 b FD(\()q Fp(x)20 b FD(+)g(1\))q(\)])25 b(=)-15 b Fn(\))25 b(8)p Fp(xA)15 b FD(\()p Fp(x)p FD(\))883 2746 y(PIND)26 b(:)f([)q Fp(A)15 b FD(\(0\))21 b Fn(^)f(8)p Fp(x)15 b FD(\()p Fp(A)g FD(\()q Fn(b)p Fp(x=)p FD(2)p Fn(c)q FD(\))26 b(=)-15 b Fn(\))25 b Fp(A)15 b FD(\()p Fp(x)p FD(\))q(\)])26 b(=)-15 b Fn(\))24 b(8)p Fp(xA)15 b FD(\()p Fp(x)p FD(\))0 2950 y(Here)37 b Fp(A)g FD(is)f(a)h(sen)m(tence)h(that)f(ma)m(y)g(con)m (tain)h(additional)f(v)-5 b(ariables.)97 b(Clearly)37 b(the)f(IND)h(axioms)h(imply)e(the)0 3063 y(PIND)29 b(ones,)g(but)f (the)g(con)m(v)m(erse)i(is)f(b)s(eliev)m(ed)g(to)g(b)s(e)f(false.)69 b(Y)-8 b(ou)29 b(can)f(think)g(of)h(PIND)f(as)h(`lazy)h(induction':)39 b(it)0 3176 y(forces)32 b(us,)f(the)h(theorem)g(pro)m(v)m(ers,)g(to)g (do)f(the)h(hard)e(w)m(ork)i(of)f(sho)m(wing)h(that)g Fp(A)15 b FD(\()p Fn(b)q Fp(x=)p FD(2)p Fn(c)q FD(\))28 b(=)-15 b Fn(\))26 b Fp(A)15 b FD(\()q Fp(x)p FD(\))31 b(for)g(all)i Fp(x)p FD(,)0 3289 y(so)e(that)g(it)f(can)h(get)h(b)m(y)e (with)g(an)g(exp)s(onen)m(tially)i(`shallo)m(w)m(er')g(induction)e (than)g(IND)q(.)141 3401 y(No)m(w,)37 b(a)e(\006)525 3415 y Fy(1)564 3401 y FD(-sen)m(tence)i(is)d(an)m(y)h(sen)m(tence)h (of)f(the)g(form)g Fn(9)p Fp(xP)27 b FD(\()q Fp(x)p FD(\),)36 b(where)e(the)h(quan)m(ti\014er)g Fn(9)p Fp(x)f FD(is)h(b)s(ounded.)0 3514 y(Lik)m(ewise,)40 b(a)d(\006)547 3528 y Fy(2)586 3514 y FD(-sen)m(tence)i(has)d(the)i(form)e Fn(9)p Fp(x)p Fn(8)p Fp(y)s(P)27 b FD(\()p Fp(x;)15 b(y)s FD(\))38 b(where)e Fn(9)p Fp(x)g FD(and)h Fn(8)p Fp(y)i FD(are)e(b)s(ounded,)g (and)f(so)i(on,)g(in)0 3627 y(analogy)43 b(to)f(the)g(p)s(olynomial)g (hierarc)m(h)m(y)g FC(PH)q FD(.)116 b(Then)40 b(the)i(theory)g(T)2569 3591 y Fo(i)2569 3650 y Fy(2)2650 3627 y FD(is)f(b)s(ounded)f (arithmetic)j(with)e(an)0 3740 y(IND)36 b(axiom)g(for)e(ev)m(ery)i (\006)935 3754 y Fo(i)963 3740 y FD(-sen)m(tence)h Fp(A)p FD(,)e(and)g(S)1720 3704 y Fo(i)1720 3763 y Fy(2)1795 3740 y FD(is)g(b)s(ounded)e(arithmetic)k(with)d(a)i(PIND)f(axiom)h(for) f(ev)m(ery)0 3853 y(\006)66 3867 y Fo(i)94 3853 y FD(-sen)m(tence)d Fp(A)p FD(.)71 b(The)30 b(theories)h(can)g(b)s(e)e(ordered)h(as)h (follo)m(ws)g(from)f(less)h(to)g(more)f(p)s(o)m(w)m(erful:)1460 4057 y(S)1510 4020 y Fy(1)1510 4080 y(2)1575 4057 y Fn(\022)25 b FD(T)1736 4020 y Fy(1)1736 4080 y(2)1801 4057 y Fn(\022)g FD(S)1947 4020 y Fy(2)1947 4080 y(2)2012 4057 y Fn(\022)g FD(T)2174 4020 y Fy(2)2174 4080 y(2)2238 4057 y Fn(\022)g(\001)15 b(\001)g(\001)0 4262 y FD(A)30 b(ma)5 b(jor)31 b(op)s(en)f(problem)f (is)i(whether)f(the)g(ab)s(o)m(v)m(e)i(inclusions)e(are)h(prop)s(er.) 141 4374 y(The)h(b)s(ounded)d(arithmetic)34 b(theories)e(are)h(w)m(eak) m(er)g(than)f(Sazano)m(v's)h(theory)f(T,)g(whic)m(h)g(w)m(e)g (considered)g(in)0 4487 y(Section)g(3.2.)77 b(Ho)m(w)m(ev)m(er,)34 b(the)d(indep)s(endence)f(results)i(that)g(can)f(b)s(e)g(sho)m(wn)g (are)h(stronger:)43 b(they)31 b(rule)g(out)h(all)0 4600 y Fq(sup)-5 b(erp)g(olynomial)42 b FD(lo)m(w)m(er)30 b(b)s(ounds,)d(not)i(just)g(exp)s(onen)m(tial)g(lo)m(w)m(er)h(b)s (ounds)d(as)i(in)g(Sazano)m(v's)h(case.)70 b(Moreo)m(v)m(er,)p 0 4679 1560 4 v 73 4733 a Fu(11)138 4765 y Ft(So)28 b(the)g(results)h (really)g(talk)f(ab)r(out)g Fl(pr)l(o)l(of-se)l(quenc)l(es)38 b Fe(f)q Fr(P)1854 4773 y Fg(n)1896 4765 y Fe(g)1935 4788 y Fg(n)p Fd(\025)p Fu(1)2055 4765 y Ft(,)29 b(only)f(indirectly)g (ab)r(out)g(pro)r(ofs.)72 b(The)28 b(notion)h(of)g(a)f(pro)r(of-)0 4871 y(sequence)e(helps)h(to)f(resolv)n(e)h(the)f(follo)n(wing)j (puzzle.)64 b(Supp)r(ose)26 b(an)n(y)g(pseudorandom)g(function)g (family)i(in)e Fs(TC)3306 4839 y Fc(0)3363 4871 y Ft(could)g(b)r(e)h (brok)n(en)0 4962 y(b)n(y)h(a)i(quan)n(tum)e(computer)h(\(not)g(so)h (implausible,)i(giv)n(en)d(that)g(the)g(only)h(candidate)f(family)-6 b(,)31 b(due)e(to)h(Naor)f(and)g(Reingold)h([40)q(],)0 5053 y(is)d(based)f(on)h(factoring)h(and)e(discrete)h(logarithm\).)64 b(Migh)n(t)27 b(w)n(e)g(then)e(ha)n(v)n(e)h(a)h(\\quan)n(tum)e(natural) i(pro)r(of")h(that)e Fs(TC)3494 5021 y Fc(0)3547 5053 y Fe(6)p Ft(=)d Fs(P)p Ft(?)53 b(The)0 5144 y(answ)n(er)26 b(is)g(that)f(at)h(b)r(est,)g(w)n(e'd)g(get)g(a)f(quan)n(tum)f(T)-6 b(uring)26 b(mac)n(hine)f(that)h(on)f(input)g Fr(n)p Ft(,)h(v)n(eri\014es)f(in)g(time)h(2)3148 5113 y Fg(O)r Fu(\()p Fg(n)p Fu(\))3313 5144 y Ft(\(sa)n(y\))f(that)g(CVP)3836 5152 y Fg(n)3879 5144 y Ft(,)0 5236 y(the)j(Circuit)g(V)-6 b(alue)28 b(Problem)g(of)h(size)g Fr(n)p Ft(,)g(requires)f Fs(TC)1649 5204 y Fc(0)1708 5236 y Ft(circuits)h(of)f(size)h Fr(n)2263 5204 y Fu(log)12 b Fg(n)2396 5236 y Ft(.)69 b(F)-6 b(or)28 b(a)g(natural)g(pro)r(of)h(of)g Fs(TC)3357 5204 y Fc(0)3413 5236 y Fe(6)p Ft(=)c Fs(P)p Ft(,)k(w)n(e'd)f(still)0 5327 y(need)d(a)h Fl(classic)l(al)34 b Ft(algorithm)27 b(to)f(break)f(pseudorandom)h(functions)g(in)g Fs(TC)2237 5295 y Fc(0)2268 5327 y Ft(.)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 0 91 a FD(as)42 b(discussed)f(earlier,)k(for)d (eac)m(h)g(particular)g Fp(n)f FD(they)h(giv)m(e)h(a)f(lo)m(w)m(er)h(b) s(ound)d(on)h(the)h(length)g(of)g(a)g(pro)s(of)f(of)0 204 y Fh(q)15 b FD(Circuit)339 218 y Fo(n)386 204 y FD(.)141 317 y(Razb)s(oro)m(v)25 b([55)q(])f(sho)m(w)m(ed)h(that)f(if)g(there)g (exists)h(a)f(pseudorandom)f(generator)i(that)g(requires)e(circuits)i (of)f(size)0 430 y(\012)81 356 y Fb(\000)122 430 y FD(2)167 397 y Fo(n)210 374 y Fg(")248 356 y Fb(\001)320 430 y FD(to)31 b(break)f(for)g(some)h Fp(")26 b(>)e FD(0)31 b(\(the)g(same)g(assumption)e(used)h(for)g(natural)g(pro)s(ofs\),)g (then)g FC(NP)c Fm(*)f FC(P)p Fp(=)p FC(p)s(oly)0 543 y FD(is)41 b(unpro)m(v)-5 b(able)41 b(in)f(the)i(theory)f(S)1208 507 y Fy(2)1208 565 y(2)1248 543 y FD(.)113 b(Indeed,)43 b(no)e(class)h(of)f(functions)g(de\014nable)f(in)h(b)s(ounded)e (arithmetic)0 656 y(can)f(then)g(b)s(e)g(pro)m(v)m(en)g(to)h(lie)g (outside)f FC(P)p Fp(=)p FC(p)s(oly)q FD(,)i(so)f(in)e(particular,)k FC(\006)2475 623 y Fk(P)2475 684 y Fo(k)2562 656 y Fm(*)d FC(P)p Fp(=)p FC(p)s(oly)h FD(is)f(unpro)m(v)-5 b(able)38 b(for)g(all)h Fp(k)s FD(.)0 769 y(Also,)c(Razb)s(oro)m(v)e(sho)m(w)m (ed)g(that)h FC(NP)c Fm(*)f FC(P)p Fp(=)p FC(p)s(oly)34 b FD(is)f(unpro)m(v)-5 b(able)33 b(in)f(S)2429 733 y Fy(1)2429 791 y(2)2468 769 y FD(,)i(under)e(the)h(w)m(eak)m(er)h (assumption)e(that)0 882 y(there)24 b(exists)g(a)g(pseudorandom)d (generator)k(computable)f(in)f(p)s(olynomial)h(time)g(that)g(requires)f (b)s(ounded)e(fan-in)0 995 y(circuits)31 b(of)f(depth)g(\012)15 b(\()p Fp(n)851 962 y Fo(")888 995 y FD(\))30 b(to)h(break)g(for)f (some)g Fp(")c(>)f FD(0.)141 1108 y(The)d(k)m(ey)g(to)h(the)f(ab)s(o)m (v)m(e)h(results)f(is)f(what's)h(called)h(the)f Fq(E\016cient)j(Interp) -5 b(olation)28 b(Pr)-5 b(op)g(erty)32 b FD(\(EIP\).)44 b(Supp)s(ose)0 1220 y(w)m(e)35 b(ha)m(v)m(e)h(a)f(conjunction)g Fp(')e FD(=)f Fp(A)15 b FD(\()q Fp(x;)g(z)t FD(\))24 b Fn(^)f Fp(B)c FD(\()q Fp(y)s(;)c(z)t FD(\))q(,)36 b(where)e Fp(x;)15 b(y)s(;)g(z)39 b FD(are)c(sets)h(of)e(v)-5 b(ariables)36 b(\()p Fp(z)j FD(b)s(eing)34 b(a)h(set)h(of)0 1333 y(`shared')30 b(v)-5 b(ariables\).)72 b(If)29 b Fp(')i FD(is)f(unsatis\014able,)g (then)g(for)g(ev)m(ery)h(\014xed)f(c)m(hoice)i(of)e Fp(z)t FD(,)h(either)f Fp(A)15 b FD(\()q Fp(x;)g(z)t FD(\))31 b(or)f Fp(B)20 b FD(\()p Fp(y)s(;)15 b(z)t FD(\))0 1446 y(m)m(ust)30 b(b)s(e)f(unsatis\014able.)70 b(Giv)m(en)30 b Fp(z)k FD(as)c(input,)f(the)h Fq(interp)-5 b(olation)35 b(pr)-5 b(oblem)39 b FD(is)30 b(to)g(return)f(whic)m(h)g(of)h Fp(A)g FD(or)g Fp(B)k FD(is)0 1559 y(unsatis\014able|or)e(if)h(b)s(oth) f(are)g(unsatis\014able,)i(then)e(either)h Fp(A)f FD(or)h Fp(B)5 b FD(.)79 b(W)-8 b(e)34 b(sa)m(y)f(a)g(pro)s(of)e(system)i Fn(S)39 b FD(satis\014es)0 1672 y(the)31 b(EIP)-8 b(,)32 b(if)f(whenev)m(er)g Fp(')g FD(has)g(a)h(p)s(olynomial-size)g (refutation)g(in)f Fn(S)7 b FD(,)31 b(there's)h(a)f(p)s(olynomial-time) i(algorithm)0 1785 y(that)e(solv)m(es)h(the)e(in)m(terp)s(olation)i (problem.)141 1898 y(What)k(Razb)s(oro)m(v)g(did)f(w)m(as)g(to)h (create)h(a)f Fp(')f FD(for)g(whic)m(h)g(solving)h(the)g(in)m(terp)s (olation)g(problem)f(is)g(as)h(hard)0 2011 y(as)c(breaking)g(a)h (pseudorandom)d(function.)77 b(Let)33 b Fp(f)41 b FD(b)s(e)31 b(a)h(pseudorandom)f(function)h(mapping)f Fp(n)3450 1978 y Fo(c)3516 2011 y FD(bits)h(to)h(2)3853 1978 y Fo(n)0 2124 y FD(bits,)e(and)e(let)j Fp(s)e FD(b)s(e)f(an)m(y)i(explicit)h (function)e(suc)m(h)g(that)1290 2328 y(Range)16 b(\()p Fp(f)10 b FD(\))20 b Fn(\\)g FD(\(Range)c(\()p Fp(f)10 b FD(\))20 b Fn(\010)g Fp(s)p FD(\))25 b(=)g Fm(?)p Fp(:)0 2532 y FD(Then)h(for)h Fp(z)i Fn(2)c(f)q FD(0)p Fp(;)15 b FD(1)p Fn(g)749 2490 y Fy(2)784 2467 y Fg(n)831 2532 y FD(,)28 b(de\014ne)e Fp(')g FD(=)f Fp(A)15 b FD(\()q Fp(z)t FD(\))f Fn(^)f Fp(B)19 b FD(\()q Fp(z)t FD(\))27 b(where)g(\(informally)-8 b(,)29 b(and)d(suppressing)f(v)-5 b(ariables)28 b(b)s(esides)0 2645 y Fp(z)t FD(\))1145 2849 y Fp(A)15 b FD(\()q Fp(z)t FD(\))26 b Fn(\()-15 b(\))24 b Fp(z)35 b FD(b)s(elongs)30 b(to)47 b(Range)15 b(\()q Fp(f)10 b FD(\))15 b Fp(;)1140 2987 y(B)k FD(\()q Fp(z)t FD(\))26 b Fn(\()-15 b(\))24 b FD(\()q Fp(z)g Fn(\010)c Fp(s)p FD(\))46 b(b)s(elongs)30 b(to)46 b(Range)16 b(\()p Fp(f)10 b FD(\))15 b Fp(:)0 3191 y FD(Clearly)32 b Fp(')g FD(is)f(unsatis\014able.)75 b(On)30 b(the)i(other)f(hand,)g (if)h(w)m(e)f(could)h(decide)f(whic)m(h)h(of)f Fp(A)h FD(or)f Fp(B)36 b FD(is)31 b(unsatis\014able)0 3304 y(\(that)i(is,)h (solv)m(e)f(the)g(in)m(terp)s(olation)h(problem\),)f(then)f(w)m(e)h (could)f(distinguish)g Fp(f)42 b FD(from)32 b(a)g(random)g(function)g (in)0 3417 y(time)26 b(2)247 3384 y Fo(O)r Fy(\()p Fo(n)p Fy(\))405 3417 y FD(.)64 b(It)25 b(follo)m(ws)i(that)e(in)g(an)m(y)h (pro)s(of)e(system)i Fn(S)32 b FD(satisfying)26 b(the)f(EIP)-8 b(,)26 b Fp(')f FD(can't)h(ha)m(v)m(e)h(a)e(p)s(olynomial-size)0 3530 y(refutation)j(assuming)f(there)h(exist)g(2)1298 3497 y Fo(n)1341 3474 y Fg(")1379 3530 y FD(-secure)f(pseudorandom)f (generators.)68 b(F)-8 b(rom)28 b(there)g(it's)g(easy)g(to)g(sho)m(w)0 3643 y(that)37 b(the)f(tautologies)i Fn(f)q Fh(q)15 b FD(Circuit)1214 3657 y Fo(n)1261 3643 y Fn(g)1307 3670 y Fo(n)p Ff(\025)p Fy(1)1480 3643 y FD(\(assuming)36 b(they)g(are)g(tautologies!\))60 b(don't)36 b(ha)m(v)m(e)h(p)s (olynomial-size)0 3756 y(pro)s(ofs)e(in)g Fn(S)7 b FD(.)93 b(As)35 b(an)h(example,)i(Pudl\023)-45 b(ak)35 b([45)q(])h(sho)m(w)m (ed)g(that)h(the)f(Cutting)g(Planes)g(pro)s(of)f(system)g(satis\014es)0 3869 y(the)d(EIP)-8 b(,)33 b(and)e(this)h(immediately)h(implies)g(that) f(Cutting)h(Planes)f(can't)h(pro)m(v)m(e)g FC(NP)28 b Fm(*)g FC(P)p Fp(=)p FC(p)s(oly)r FD(,)k(again)h(under)0 3982 y(the)e(pseudorandomness)d(assumption.)141 4095 y(So)k(EIP)f(is)h(a)h(useful)e(prop)s(ert)m(y)-8 b(,)32 b(since)g(it)h(immediately)g(giv)m(es)g(us)e(conditional)j(lo)m(w)m(er) f(b)s(ounds)d(on)h(a)i(pro)s(of)0 4208 y(system's)k(abilit)m(y)h(to)g (pro)m(v)m(e)f(circuit)g(lo)m(w)m(er)h(b)s(ounds.)95 b(Th)m(us,)37 b(man)m(y)g(researc)m(hers)g(hop)s(ed)f(to)h(sho)m(w)g (the)f(EIP)0 4320 y(for)d(stronger)h(pro)s(of)f(systems,)h(esp)s (ecially)h(the)f(so-called)h(Extended)e(F)-8 b(rege)35 b(\()p Fn(E)8 b(F)i FD(\))33 b(system.)84 b(Unfortunately)-8 b(,)0 4433 y(Kra)5 b(j)-10 b(\023)-35 b(\020)m(\024)-43 b(cek)40 b(and)e(Pudl\023)-45 b(ak)38 b([31)q(])g(sho)m(w)m(ed)h(that)g (the)g(EIP)f(fails)h(for)f(this)g(system|ironically)-8 b(,)43 b(under)37 b(a)h(crypto-)0 4546 y(graphic)31 b(assumption)f(lik) m(e)i(those)g(used)e(to)h(pro)m(v)m(e)h(lo)m(w)m(er)g(b)s(ounds)c(on)j (pro)s(of)f(size!)74 b(The)30 b(idea)h(is)g(simple:)42 b(they)0 4659 y(created)31 b(a)g(disjunction)f Fp(')c FD(=)f Fp(A)15 b FD(\()p Fp(z)t FD(\))21 b Fn(^)f Fp(B)g FD(\()p Fp(z)t FD(\))31 b(where)f(\(again)h(informally\))1067 4863 y Fp(A)15 b FD(\()q Fp(z)t FD(\))26 b Fn(\()-15 b(\))24 b Fp(z)35 b FD(is)30 b(an)h(RSA)f(encryption)g(of)g(a)h(0)g (bit,)1062 5001 y Fp(B)19 b FD(\()q Fp(z)t FD(\))26 b Fn(\()-15 b(\))24 b Fp(z)35 b FD(is)30 b(an)h(RSA)f(encryption)g(of)g (a)h(1)g(bit.)0 5205 y(Clearly)41 b Fp(')g FD(is)g(unsatis\014able.)111 b(Moreo)m(v)m(er,)46 b(using)40 b(some)h(n)m(um)m(b)s(er-theoretic)g (facts,)j(Kra)5 b(j)-10 b(\023)-35 b(\020)m(\024)-43 b(cek)42 b(and)e(Pudl\023)-45 b(ak)0 5318 y(sho)m(w)m(ed)28 b(that)g(this)g(unsatis\014abilit)m(y)g(can)g(b)s(e)f Fq(pr)-5 b(oven)36 b FD(in)27 b(the)h(theories)g(T)2529 5283 y Fy(3)2529 5341 y(2)2596 5318 y FD(and)f(S)2820 5283 y Fy(1)2820 5341 y(2)2875 5318 y FD(+\010,)g(where)h(\010)f(is)g (the)h(axiom)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 0 91 a FD(that)40 b(an)m(y)g(in)m(teger)h(ha)m (ving)f(a)g(Pratt)g(certi\014cate)1724 58 y Fy(12)1840 91 y FD(is)f(prime.)107 b(This)39 b(implies)g(in)h(particular)f(that)h Fp(')g FD(has)g(a)0 204 y(p)s(olynomial-size)35 b(refutation)f(in)f Fn(E)8 b(F)h FD(.)83 b(It)33 b(follo)m(ws)h(that,)h(if)e Fn(E)8 b(F)43 b FD(satis\014ed)34 b(the)f(EIP)-8 b(,)33 b(then)g(there)h(w)m(ould)f(b)s(e)g(a)0 317 y(p)s(olynomial)23 b(time)h(algorithm)g(to)g(solv)m(e)g(the)f(in)m(terp)s(olation)i (problem)d(and)h(thereb)m(y)g(break)g(RSA.)45 b(W)-8 b(e)25 b(conclude)0 430 y(that)31 b Fn(E)8 b(F)40 b FD(do)s(esn't)30 b(satisfy)h(the)f(EIP)-8 b(,)31 b(assuming)f(RSA)g(is)g(secure.)141 543 y(I'll)d(conclude)g(with)g(one)g(example)g(of)g(an)g Fq(unc)-5 b(onditional)38 b FD(`second-generation')29 b(indep)s(endence)d(result.)66 b(In)0 656 y(the)36 b(w)m(ell-kno)m(wn)g (resolution)h(pro)s(of)e(system,)i(w)m(e're)g(giv)m(en)f(a)g(set)h(of)e (CNF)h(clauses)h(that)f(w)m(e)g(w)m(an)m(t)h(to)f(pro)m(v)m(e)0 769 y(unsatis\014able.)97 b(The)37 b(allo)m(w)m(ed)i(op)s(eration)e(is) g(to)h(\\smash)f(together")h(t)m(w)m(o)h(previous)d(clauses,)k(of)d (whic)m(h)g(one)0 882 y(con)m(tains)24 b(a)f(literal)h Fp(a)f FD(and)f(the)h(other)g(con)m(tains)h Fh(q)p Fp(a)p FD(,)h(to)e(deriv)m(e)g(a)g(new)f(clause.)62 b(F)-8 b(or)24 b(example,)h(giv)m(en)e(the)g(clauses)0 995 y(\()p Fp(a)p Fn(_)p Fh(q)p Fp(b)p FD(\))31 b(and)e(\()p Fh(q)p Fp(a)21 b Fn(_)f Fp(c)g Fn(_)g Fp(d)p FD(\))31 b(w)m(e)f(can)g(deriv)m(e)h(\()p Fh(q)p Fp(b)21 b Fn(_)f Fp(c)g Fn(_)g Fp(d)p FD(\))q(.)70 b(The)30 b Fq(length)37 b FD(of)30 b(a)g(resolution)h(pro)s(of)e(is)h (the)g(n)m(um)m(b)s(er)0 1108 y(of)g(clauses)h(it)f(deriv)m(es)h(prior) e(to)i(the)f(empt)m(y)g(clause.)71 b(Hak)m(en)31 b([23)q(])f(sho)m(w)m (ed)h(the)f(\014rst)f(sup)s(erp)s(olynomial)g(lo)m(w)m(er)0 1220 y(b)s(ound)g(on)i(the)g(lengths)g(of)h(resolution)f(refutations.) 74 b(The)31 b(unsatis\014able)g(form)m(ulas)g(he)g(used)f(w)m(ere)h (based)g(on)0 1333 y(the)g(Pigeonhole)h(Principle;)g(they)f(enco)s(ded) f(that)i Fp(n)20 b FD(+)g(1)31 b(pigeons)g(are)h(eac)m(h)g(in)e(one)h (of)g Fp(n)g FD(holes,)g(with)g(no)g(t)m(w)m(o)0 1446 y(pigeons)k(in)g(the)g(same)g(hole.)90 b(In)m(tuitiv)m(ely)-8 b(,)38 b(with)c(resolution)i(w)m(e're)f(stuc)m(k)h(reasoning)f Fq(lo)-5 b(c)g(al)5 b(ly)j FD(:)52 b(\\let's)36 b(see,)h(if)0 1559 y(w)m(e)f(put)f(this)h(pigeon)g(here,)i(and)d(mo)m(v)m(ed)i(that)f (one)g(there.)16 b(.)f(.)h(darn,)36 b(still)h(do)s(esn't)f(w)m(ork!")72 b(Resolution)37 b(isn't)0 1672 y(p)s(o)m(w)m(erful)d(enough)f(to)i Fq(c)-5 b(ount)43 b FD(the)34 b(pigeons)h(and)e(the)h(holes,)h(and)f (see)g(that)h(the)f(former)g(are)g(more)g(n)m(umerous)0 1785 y(than)c(the)h(latter.)141 1898 y(Recen)m(tly)36 b(Raz)f([47)q(])f(impro)m(v)m(ed)h(Hak)m(en's)g(result)f(to)h(sho)m(w)f (that)h(ev)m(en)g(form)m(ulas)f(based)g(on)g(the)g(so-called)0 2011 y(`W)-8 b(eak)31 b(On)m(to)f(Pigeonhole)h(Principle'|that)f Fp(m)25 b Fn(\035)g Fp(n)k FD(pigeons)h(can't)g(b)s(e)f(assigned)g(to)h Fp(n)f FD(holes,)h(with)f(exactly)0 2124 y(one)f(pigeon)h(in)f(ev)m (ery)h(hole|require)f(resolution)h(refutations)g(of)f(size)h(2)2538 2091 y Fo(n)2581 2067 y Fg(")2647 2124 y FD(for)f(some)h Fp(")c(>)g FD(0.)69 b(By)28 b(a)h(reduction)0 2237 y(originally)43 b(due)f(to)g(Razb)s(oro)m(v)h([51)q(],)i(a)e(corollary)g(is)f(that)g (the)g(set)h(of)f(form)m(ulas)g Fn(f)p FD(Circuit)3278 2251 y Fo(n)3325 2237 y Fn(g)3371 2263 y Fo(n)p Ff(\025)p Fy(1)3550 2237 y FD(\(under)f(a)0 2350 y(natural)31 b(prop)s(ositional) g(enco)s(ding\),)g(enco)s(ding)f(that)i(SA)-8 b(T)30 b(has)g(small)h(circuits,)h(don't)f(ha)m(v)m(e)g(p)s(olynomial-size)0 2462 y(resolution)d(refutations.)68 b(In)m(tuitiv)m(ely)-8 b(,)30 b(consider)e(a)g(small)g(DNF)g(form)m(ula)g(where)f(eac)m(h)i (clause)f(con)m(tains)h(ev)m(ery)0 2575 y(v)-5 b(ariable)42 b(\(either)g(negated)g(or)g(non-negated\).)116 b(Though)40 b(it)i(seems)f(ob)m(vious)h(that)g(suc)m(h)f(a)h(form)m(ula)f(can't)0 2688 y(compute)c(SA)-8 b(T,)36 b(one)g(do)s(es)g(need)g(to)i(sho)m(w)e (that)h(there)f(are)h(more)f(`y)m(es')i(instances)f(of)f(SA)-8 b(T)36 b(than)g(there)h(are)0 2801 y(clauses)31 b(in)f(the)h(DNF|and)f (that)h(requires)f(the)h(W)-8 b(eak)32 b(On)m(to)f(Pigeonhole)g (Principle!)141 2914 y(Impro)m(ving)g(on)h(Raz's)g(result,)g(Razb)s (oro)m(v)g(has)g(sho)m(wn)f([54)q(])g(that)h Fh(q)15 b FD(Circuit)2791 2928 y Fo(n)2870 2914 y FD(has)31 b(no)g(succinct)h (resolution)0 3027 y(pro)s(ofs)f(ev)m(en)i(when)f(the)g(circuits)h(in)f (the)h(enco)s(ding)f(ha)m(v)m(e)i(b)s(ounded)c(fan-in.)46 b(Using)33 b(a)f(di\013eren)m(t)h(reduction|)0 3140 y(based)23 b(on)g(the)g(Nisan-Wigderson)h(pseudorandom)e(generator)i([41)q(],)h (rather)e(than)g(the)g(pigeonhole)h(principle|)0 3253 y(Razb)s(oro)m(v)34 b(has)f(also)h(sho)m(wn)f([53)q(])g(that)h Fh(q)15 b FD(Circuit)1753 3267 y Fo(n)1833 3253 y FD(has)33 b(no)g(succinct)h(pro)s(ofs)e(in)h(sev)m(eral)h(extensions)g(of)f (reso-)0 3366 y(lution,)g(including)e(PCR)h(\(P)m(olynomial)i(Calculus) e(and)f(Resolution\))i(and)f Fp(k)s FD(-DNF)h(resolution,)g(or)f (resolution)0 3479 y(with)e Fp(k)s FD(-DNF's)i(instead)f(of)f(clauses,) h(for)g Fp(k)d FD(=)d Fp(")15 b FD(log)j Fp(n)p FD(.)141 3592 y(T)-8 b(aking)28 b(a)g(step)f(bac)m(k,)i(do)f(these)f(results)h (tell)g(us)f(an)m(ything)h(ab)s(out)f FC(P)g FD(vs.)h FC(NP)p FD(|for)f(example,)i(whether)e(the)0 3704 y(problem)33 b(is)g(lik)m(ely)i(to)f(b)s(e)e(indep)s(enden)m(t)g(of)i(ZF)f(or)g (some)h(other)f(strong)h(theory?)82 b(In)33 b(the)g(app)s(endix)f(of)h ([48)q(],)0 3817 y(Razb)s(oro)m(v)28 b(argues)f(that)h(all)g(kno)m(wn)f (\\explicit")j(tec)m(hniques)e(for)f(circuit)g(lo)m(w)m(er)i(b)s(ounds) c(can)j(b)s(e)e(formalized)i(in)0 3930 y(S)51 3894 y Fy(1)51 3953 y(2)90 3930 y FD(.)59 b(Therefore,)23 b(the)f(inabilit)m (y)h(ev)m(en)f(of)g(S)1445 3894 y Fy(2)1445 3953 y(2)1506 3930 y FD(to)g(pro)m(v)m(e)h FC(NP)i Fm(*)g FC(P)p Fp(=)p FC(p)s(oly)e FD(under)d(a)i(pseudorandomness)d(assumption)0 4043 y(could)30 b(b)s(e)g(tak)m(en)i(as)e(strong)h(evidence)g(that)g (those)g(tec)m(hniques)g(are)g(logically)i(to)s(o)e(w)m(eak)g(to)g(pro) m(v)m(e)g FC(P)26 b Fn(6)p FD(=)f FC(NP)p FD(.)141 4156 y(On)c(the)i(other)f(hand,)h(a)g(telling)g(p)s(oin)m(t,)h(men)m(tioned) f(in)f([48)q(],)i(is)e(that)h(S)2545 4120 y Fy(1)2545 4179 y(2)2607 4156 y FD(can't)g(ev)m(en)g(formalize)g(the)g(Shannon)0 4269 y(coun)m(ting)i(argumen)m(t,)i(whic)m(h)d(sho)m(ws)h(that)g (almost)g(all)h(Bo)s(olean)g(functions)e(require)g(exp)s(onen)m (tial-size)j(circuits.)0 4382 y(As)37 b(a)g(consequence,)i(S)819 4346 y Fy(1)819 4404 y(2)895 4382 y FD(can't)f(formalize)g(Kannan's)e (result)g([29)q(])h(that)g FC(NP)2701 4345 y Fk(EXP)2875 4382 y Fm(*)e FC(P)p Fp(=)p FC(p)s(oly)r FD(,)j(whic)m(h)f(uses)f(the)0 4495 y(Shannon)d(coun)m(ting)j(argumen)m(t;)i(or)d(the)g(Buhrman-F)-8 b(ortno)m(w-Thierauf)34 b(result)h([8)q(])g(that)g FC(MA)3337 4510 y Fk(EXP)3508 4495 y Fm(*)d FC(P)p Fp(=)p FC(p)s(oly)r FD(,)0 4608 y(whic)m(h)h(in)g(turn)e(uses)i(Kannan's)f(result.)82 b(It's)33 b(clear,)i(then,)f(that)f(there)h(exist)g(tec)m(hniques)f (not)g(formalizable)0 4721 y(in)39 b(S)166 4685 y Fy(1)166 4743 y(2)205 4721 y FD(,)j(that)e(to)g(us)f(h)m(umans)f(are)i(almost)h (the)f(epitome)g(of)g(trivialit)m(y)h(\(unlik)m(e)f(man)m(y)g(tec)m (hniques)g(that)g Fq(ar)-5 b(e)0 4834 y FD(formalizable)36 b(in)e(S)678 4798 y Fy(1)678 4856 y(2)717 4834 y FD(!\).)89 b(Whether)35 b(a)g(theorem)g(can)g(b)s(e)e(pro)m(v)m(en)i(in)g(a)g(w)m (eak)g(fragmen)m(t)h(of)e(arithmetic)i(migh)m(t)0 4946 y(not)e(sa)m(y)g(m)m(uc)m(h)f(ab)s(out)g(the)h(theorem's)g(conceptual)g (di\016cult)m(y)-8 b(.)84 b(In)33 b(one)h(of)f(the)h(man)m(y)f(ironies) h(of)f FC(P)h FD(vs.)f FC(NP)q FD(,)p 0 5026 1560 4 v 73 5079 a Fu(12)138 5111 y Ft(Pratt)21 b([44)q(])h(sho)n(w)n(ed)f(that) f Fa(Primes)j Fe(2)f Fr(N)8 b(P)j Ft(;)22 b(that)f(is,)h(ev)n(ery)e (prime)h(has)g(a)h(succinct)e(pro)r(of)i(of)g(primalit)n(y)-6 b(.)53 b(An)20 b(ob)n(vious)h(question)0 5202 y(is)27 b(whether)f(the)g(deterministic)h(primalit)n(y)g(test)f(of)i(Agra)n(w)n (al,)g(Ka)n(y)n(al,)f(and)f(Saxena)g([1])h(migh)n(t)f(eliminate)i(the)e (need)g(for)h(\010.)63 b(This)0 5294 y(seems)26 b(unlik)n(ely)-6 b(,)25 b(since)i(one)e(w)n(ould)h(still)h(need)e(to)h Fl(pr)l(ove)33 b Ft(the)25 b(correctness)i(of)f(the)g(AKS)e(algorithm)j (in)f(S)3120 5262 y Fu(1)3120 5307 y(2)3154 5294 y Ft(.)p eop end %%Page: 15 15 TeXDict begin 15 14 bop 0 91 a FD(it's)37 b(conceiv)-5 b(able)38 b(that)f(the)f(indep)s(endence)f(results)h(will)h(ultimately) g(con)m(tribute)g(to)g(pro)m(ving)g FC(P)e Fn(6)p FD(=)f FC(NP)q FD(,)k(not)0 204 y(b)s(ecause)e(of)h(what)g(they)f(tell)i(us,)f (but)f(b)s(ecause)h(of)f(the)h(lo)m(w)m(er)h(b)s(ound)c(tec)m(hniques)j (dev)m(elop)s(ed)g(to)g(pro)m(v)m(e)h(the)0 317 y(indep)s(endence)29 b(results)h(themselv)m(es!)0 604 y FE(5)135 b(Pro)l(ving)45 b(Indep)t(endence)0 807 y FD(Ultimately)-8 b(,)51 b(of)45 b(course,)k(w)m(e'd)c(w)m(an)m(t)h(to)f(pro)m(v)m(e)h FC(P)f FD(vs.)g FC(NP)g FD(indep)s(enden)m(t)f(of)h(a)g(strong)g (theory)-8 b(,)49 b(one)c(that)0 919 y(encompasses)33 b(all)h(\\ordinary")f(mathematical)i(reasoning)e(\(or)g(at)h(least)g(a) f(large)h(c)m(h)m(unk)e(of)h(it\).)82 b(But)33 b(there's)0 1032 y(a)43 b(reason)f(that's)h(probably)e(imp)s(ossible)h(with)g (curren)m(t)f(tec)m(hniques,)46 b(whic)m(h)c(w)m(as)h(p)s(oin)m(ted)f (out)g(b)m(y)g(Kurtz,)0 1145 y(O'Donnell,)31 b(and)f(Ro)m(y)m(er)i([33) q(],)f(and)e(\(indep)s(enden)m(tly\))i(Ben-Da)m(vid)h(and)d(Halevi)j ([6)q(].)141 1258 y(Let's)25 b(de\014ne)f(a)h(\005)754 1272 y Fy(1)793 1258 y FD(-sen)m(tence)h(to)f(b)s(e)f(an)m(y)h(sen)m (tence)h(of)e(the)h(form,)g(\\F)-8 b(or)26 b(all)f Fp(x)p FD(,)h Fp(P)i FD(\()p Fp(x)p FD(\))q(,")d(where)e Fp(P)38 b FD(is)24 b(function)0 1371 y(that)33 b(can)h(b)s(e)e(pro)m(v)m(en)h (to)h(b)s(e)e(recursiv)m(e)h(in)g(P)m(eano)h(Arithmetic,)g(P)-8 b(A)q(.)81 b(\(That)33 b(is,)h(there's)f(a)g(T)-8 b(uring)32 b(mac)m(hine)0 1484 y Fp(M)50 b FD(that)41 b(computes)f Fp(P)13 b FD(,)42 b(together)g(with)e(a)g(pro)s(of)f(in)h(P)-8 b(A)40 b(that)h Fp(M)50 b FD(halts)40 b(on)g(ev)m(ery)h(input.\))109 b(Similarly)-8 b(,)44 b(a)0 1597 y(\005)68 1611 y Fy(2)108 1597 y FD(-sen)m(tence)31 b(has)f(the)h(form)f Fn(8)p Fp(x)p Fn(9)p Fp(y)h(P)e FD(\()p Fp(x;)15 b(y)s FD(\))31 b(where)e Fp(P)44 b FD(is)30 b(pro)m(v)-5 b(ably)30 b(recursiv)m(e,)h (a)g(\005)2966 1611 y Fy(3)3005 1597 y FD(-sen)m(tence)h(has)e(the)g (form)0 1710 y Fn(8)p Fp(x)p Fn(9)p Fp(y)s Fn(8)p Fp(z)j(P)28 b FD(\()p Fp(x;)15 b(y)s(;)g(z)t FD(\))r(,)30 b(and)g(so)h(on.)141 1823 y(An)j(am)m(using)h(exercise)h(is)f(to)h(classify)f(famous)f (unsolv)m(ed)h(math)g(problems)f(b)m(y)g(`quan)m(ti\014er)h(complexit)m (y)-8 b(.')0 1936 y(Goldbac)m(h's)30 b(Conjecture)f(is)h(\005)1087 1950 y Fy(1)1126 1936 y FD(,)g(since)f(w)m(e)h(can)f(write)h(a)f (simple)h(predicate)g(that)f(c)m(hec)m(ks)i(whether)d(an)i(in)m(teger)0 2049 y(is)k(a)g(sum)f(of)g(t)m(w)m(o)i(primes.)84 b(The)33 b(Twin)g(Primes)g(Conjecture)h(is)g(\005)2392 2063 y Fy(2)2431 2049 y FD(:)48 b(for)33 b(all)i Fp(n)p FD(,)f(there)g(exists) g(a)g Fp(p)d(>)f(n)j FD(suc)m(h)0 2161 y(that)g Fp(p)g FD(and)f Fp(p)21 b FD(+)g(2)34 b(are)f(prime.)79 b(T)-8 b(o)33 b(mak)m(e)h(this)e(a)i(\005)1883 2175 y Fy(1)1922 2161 y FD(-sen)m(tence,)h(w)m(e'd)e(need)f(to)i(strengthen)e(the)h (conjecture)0 2274 y(b)m(y)26 b(including)h(an)f(explicit)i(lo)m(w)m (er)g(b)s(ound|sa)m(y)-8 b(,)27 b(that)g(there)g(are)g(at)g(least)h (log)17 b(log)h(log)f Fp(n)27 b FD(t)m(win)f(primes)g(less)h(than)0 2387 y Fp(n)p FD(.)69 b(The)28 b(complexit)m(y)j(of)e(the)g(Riemann)g (Hyp)s(othesis)g(\(RH\))h(is)f(less)g(ob)m(vious.)70 b(But)29 b(a)g(result)g(of)g(Lagarias)i([34)q(])0 2500 y(sho)m(ws)c(that)h(RH)g(is)f(equiv)-5 b(alen)m(t)29 b(to)g(the)e(assertion)i(that)f(for)f(all)h(p)s(ositiv)m(e)h(in)m (tegers)g Fp(n)p FD(,)f(the)f(sum)g(of)h(the)f(divisors)0 2613 y(of)k Fp(n)e FD(is)i(at)g(most)1473 2726 y Fp(\013)15 b FD(\()q Fp(n)p FD(\))25 b(=)g Fp(H)1869 2740 y Fo(n)1936 2726 y FD(+)19 b Fp(e)2068 2688 y Fo(H)2126 2696 y Fg(n)2189 2726 y FD(ln)14 b Fp(H)2355 2740 y Fo(n)2402 2726 y Fp(;)0 2893 y FD(where)24 b Fp(H)333 2907 y Fo(n)405 2893 y FD(=)h(1)9 b(+)646 2857 y Fy(1)p 646 2872 36 4 v 646 2924 a(2)700 2893 y FD(+)g Fn(\001)15 b(\001)g(\001)c FD(+)989 2857 y Fy(1)p 986 2872 43 4 v 986 2924 a Fo(n)1063 2893 y FD(is)25 b(the)g Fp(n)1355 2860 y Fo(th)1450 2893 y FD(harmonic)g(n)m(um)m(b)s(er.)62 b(This)24 b(assertion)i(is)f(\005) 2964 2907 y Fy(1)3004 2893 y FD(,)h(since)f(w)m(e)g(can)h(compute)0 3006 y(increasingly)31 b(go)s(o)s(d)f(upp)s(er)f(b)s(ounds)f(on)i Fp(\013)16 b FD(\()p Fp(n)p FD(\),)31 b(do)m(v)m(etailing)i(o)m(v)m(er) f(all)f Fp(n)p FD(.)141 3119 y(The)43 b(problem)f(that)h(concerns)g (us,)j FC(P)d FD(vs.)g FC(NP)q FD(,)g(is)g(of)g(course)g(\005)2479 3133 y Fy(2)2518 3119 y FD(:)66 b(for)43 b(all)h(T)-8 b(uring)42 b(mac)m(hines)i Fp(M)53 b FD(and)0 3232 y(p)s(olynomial)26 b(time)h(b)s(ounds)d Fp(p)p FD(,)i(there)g(exists)h(a)f(SA)-8 b(T)26 b(instance)h Fp(')f FD(suc)m(h)f(that)i Fp(M)36 b FD(do)s(esn't)26 b(halt)g(with)g(the)g(correct)0 3344 y(answ)m(er)g(to)g Fp(')g FD(in)g(at)g(most)g Fp(p)15 b FD(\()p Fp(n)p FD(\))26 b(steps,)h(where)e Fp(n)g FD(is)h(the)g(size) g(of)g Fp(')p FD(.)65 b(The)26 b FC(NP)g FD(vs.)f FC(P)p Fp(=)p FC(p)s(oly)i FD(problem)f(is)f(similarly)0 3457 y(\005)68 3471 y Fy(2)108 3457 y FD(.)141 3570 y(What)j(Kurtz)f(et)h (al.)40 b(and)27 b(Ben-Da)m(vid)h(and)f(Halevi)i(noticed)f(is)f(that)h (despite)f(b)s(eing)g(a)g(\005)3251 3584 y Fy(2)3291 3570 y FD(-sen)m(tence,)j FC(P)d FD(vs.)0 3683 y FC(NP)34 b FD(can)g(b)s(e)f(extremely)h(w)m(ell)h(\\appro)m(ximated")g(b)m(y)e (\005)1930 3697 y Fy(1)1970 3683 y FD(-sen)m(tences.)85 b(F)-8 b(or)34 b(example,)i(let)e Fp(A)g FD(b)s(e)f(the)g(assertion)0 3796 y(that)42 b(\\SA)-8 b(T)42 b(do)s(es)f(not)g(ha)m(v)m(e)i (circuits)f(of)g(size)g Fp(n)1764 3763 y Fy(log)12 b Fo(n)1913 3796 y FD(.")84 b(Then)40 b Fp(A)i FD(is)f(\005)2595 3810 y Fy(1)2635 3796 y FD(,)j(since)e(for)f(eac)m(h)i Fp(n)p FD(,)h(w)m(e)e(can)g(just)0 3909 y(searc)m(h)32 b(exhaustiv)m(ely)h(through)e(all)h(circuits)g(of)g(size)g Fp(n)1924 3876 y Fy(log)13 b Fo(n)2105 3909 y FD(and)31 b(see)h(whether)f(an)m(y)h(of)g(them)f(computes)h(SA)-8 b(T.)0 4022 y(Moreo)m(v)m(er,)33 b Fp(A)d FD(implies)h FC(P)25 b Fn(6)p FD(=)g FC(NP)q FD(,)30 b(and)g(is)g(v)m(ery)h(lik)m (ely)h Fq(true)37 b FD(\(w)m(e'd)31 b(imagine\))h(assuming)e FC(P)25 b Fn(6)p FD(=)g FC(NP)q FD(.)141 4135 y(No)m(w)d(assuming)f(P) -8 b(A)22 b(is)f(consisten)m(t,)k(w)m(e)d(can't)g(pro)m(v)m(e)g(a)g (\005)2106 4149 y Fy(1)2145 4135 y FD(-sen)m(tence)h(indep)s(enden)m(t) d(of)i(P)-8 b(A)21 b(without)h(pro)m(ving)0 4248 y(the)g(sen)m (tence|since)h(if)e(the)h(sen)m(tence)h(w)m(ere)f(false,)i(it)f(w)m (ould)e(ha)m(v)m(e)i(a)f(simple)f(coun)m(terexample!)61 b(\(In)21 b(Ap)s(ostolos)0 4361 y(Do)m(xiadis')30 b(no)m(v)m(el)f Fq(Uncle)h(Petr)-5 b(os)31 b(and)g(Goldb)-5 b(ach's)33 b(Conje)-5 b(ctur)g(e)35 b FD([17)r(],)28 b(the)g(brillian)m(t)h(Uncle) g(P)m(etros)f(misses)g(this)0 4474 y(p)s(oin)m(t)i(completely)i(while)f (m)m(using)f(ab)s(out)g(whether)g(Goldbac)m(h's)h(Conjecture)f(is)h (formally)g(indep)s(enden)m(t.\))141 4587 y(There's)40 b(a)h(further)e(p)s(oin)m(t,)k(ho)m(w)m(ev)m(er.)112 b(With)41 b(the)f(exception)i(of)e(G\177)-45 b(odel's)41 b(Incompleteness)g(Theorem,)0 4699 y(all)d(the)g(tec)m(hniques)g(w)m(e) g(ha)m(v)m(e)g(for)g(pro)m(ving)f(indep)s(endence)f(from)h(P)-8 b(A)38 b(actually)h(pro)m(v)m(e)f(indep)s(endence)e(from)0 4812 y(a)42 b(stronger)g(theory)-8 b(,)46 b(P)-8 b(A)15 b(+\005)1047 4826 y Fy(1)1087 4812 y FD(.)116 b(This)41 b(theory)h(consists)g(of)g(P)-8 b(A)42 b(augmen)m(ted)h(b)m(y)f(the)g (set)g(of)g(all)g Fq(true)49 b FD(\005)3830 4826 y Fy(1)3870 4812 y FD(-)0 4925 y(sen)m(tences.)33 b(Since)f(the)g(true)g(\005)1083 4939 y Fy(1)1122 4925 y FD(-sen)m(tences)h(can't)g(ev)m(en)f(b)s(e)g (recursiv)m(ely)g(en)m(umerated,)h(ob)m(viously)f(P)-8 b(A)16 b(+\005)3768 4939 y Fy(1)3839 4925 y FD(is)0 5038 y(an)33 b(unrealistically)i(p)s(o)m(w)m(erful)e(theory)-8 b(.)84 b(Despite)34 b(its)g(p)s(o)m(w)m(er,)g(though,)g(it)g(turns)e (out)h(to)i(b)s(e)d(unable)h(to)h(pro)m(v)m(e)0 5151 y(ev)m(en)d(some)g(simple)f(\005)786 5165 y Fy(2)826 5151 y FD(-sen)m(tences.)p eop end %%Page: 16 16 TeXDict begin 16 15 bop 141 91 a FD(As)32 b(an)g(example,)h(consider)f (Go)s(o)s(dstein's)g(Theorem)f([22)r(].)77 b(W)-8 b(e)33 b(write)f(a)g(p)s(ositiv)m(e)h(in)m(teger)g Fp(n)f FD(\(sa)m(y)h(40\))g (as)0 204 y(a)e(sum)e(of)i(p)s(o)m(w)m(ers)f(of)h(2,)g(then)f(write)g (the)h(exp)s(onen)m(ts)f(as)h(sums)e(of)h(p)s(o)m(w)m(ers)h(of)f(2,)h (and)f(so)h(on:)1348 408 y(40)26 b(=)f(2)1605 371 y Fy(5)1665 408 y FD(+)20 b(2)1801 371 y Fy(3)1866 408 y FD(=)25 b(2)2007 371 y Fy(2)2042 347 y Fu(2)2077 371 y Fy(+2)2167 347 y Fu(0)2226 408 y FD(+)20 b(2)2362 371 y Fy(2+2)2487 347 y Fu(0)2527 408 y Fp(:)0 613 y FD(\(This)33 b(is)g(called)h(the)f (base-2)h Fq(her)-5 b(e)g(ditary)38 b(r)-5 b(epr)g(esentation.)p FD(\))85 b(Then)32 b(w)m(e)h(c)m(hange)h(all)g(the)g(2's)f(to)h(3's)g (to)f(obtain)0 726 y(3)45 693 y Fy(3)80 669 y Fu(3)115 693 y Fy(+3)205 669 y Fu(0)264 726 y FD(+)20 b(3)400 693 y Fy(3+3)525 669 y Fu(0)565 726 y FD(,)31 b(then)f(subtract)g(1)h (and)f(re-express)g(in)g(base-3)h(hereditary)f(represen)m(tation:)250 930 y(3)295 892 y Fy(3)330 869 y Fu(3)366 892 y Fy(+3)456 869 y Fu(0)515 930 y FD(+)20 b(3)651 892 y Fy(3+3)776 869 y Fu(0)836 930 y Fn(\000)g FD(1)25 b(=)g(22)p Fp(;)15 b FD(876)g Fp(;)g FD(792)p Fp(;)g FD(455)q Fp(;)g FD(04)q(1)32 b(=)25 b(3)2073 892 y Fy(3)2108 869 y Fu(3)2143 892 y Fy(+3)2233 869 y Fu(0)2292 930 y FD(+)20 b(2)h Fn(\001)f FD(3)2539 892 y Fy(3)2599 930 y FD(+)g(2)h Fn(\001)f FD(3)2846 892 y Fy(2)p Ff(\001)p Fy(3)2936 869 y Fu(0)2996 930 y FD(+)g(2)g Fn(\001)h FD(3)3243 892 y Fy(3)3278 869 y Fu(0)3337 930 y FD(+)f(2)h Fn(\001)f FD(3)3584 892 y Fy(0)3624 930 y Fp(:)0 1134 y FD(Then)33 b(w)m(e)i(c)m(hange)h (all)f(the)g(3's)g(to)g(4's,)h(subtract)f(1,)h(re-express)e(in)g (base-4)h(hereditary)g(represen)m(tation,)i(and)0 1247 y(so)43 b(on,)j(increasing)e(the)f(base)g(b)m(y)f(1)h(eac)m(h)h(time.) 122 b(Surprisingly)-8 b(,)45 b(b)m(y)d(an)h(argumen)m(t)g(in)m(v)m (olving)i(coun)m(table)0 1360 y(ordinals,)29 b(Go)s(o)s(dstein)f(sho)m (w)m(ed)g(that)h(no)f(matter)g(what)g Fp(n)g FD(w)m(e)g(start)h(with,)f (this)g(pro)s(cess)g(will)g(alw)m(a)m(ys)i(con)m(v)m(erge)0 1473 y(to)f(0.)69 b(Subsequen)m(tly)28 b(P)m(aris)h(and)f(Harrington)g ([42)r(])g(sho)m(w)m(ed)h(that)g(Go)s(o)s(dstein's)g(Theorem)f(is)h (indep)s(enden)m(t)e(of)0 1586 y(P)-8 b(A|meaning)31 b(that)g(the)g(use)f(of)g(coun)m(table)i(ordinals)e(w)m(as)h(necessary) -8 b(.)141 1699 y(Clearly)34 b(Go)s(o)s(dstein's)f(Theorem)g(is)g(\005) 1508 1713 y Fy(2)1548 1699 y FD(:)46 b(for)33 b(all)h Fp(n)p FD(,)f(there)g(exists)h(a)g Fp(t)f FD(suc)m(h)f(that)i(the)f (pro)s(cess)g(con)m(v)m(erges)0 1812 y(in)h Fp(t)h FD(steps)f(if)h(w)m (e)g(start)g(with)f Fp(n)p FD(.)88 b(What)35 b(P)m(aris)g(and)f (Harrington)h(actually)i(sho)m(w)m(ed)d(w)m(as)h(that)h(Go)s(o)s (dstein's)0 1924 y(Theorem)31 b(is)h(indep)s(enden)m(t)e(of)i(P)-8 b(A)16 b(+\005)1376 1938 y Fy(1)1415 1924 y FD(|in)31 b(other)h(w)m(ords,)g(ev)m(en)g(if)f(w)m(e)h(threw)f(in)h(all)g(true)g (\005)3323 1938 y Fy(1)3362 1924 y FD(-sen)m(tences)h(for)0 2037 y(free,)f(the)g(theorem)g(w)m(ould)g Fq(stil)5 b(l)41 b FD(b)s(e)31 b(unpro)m(v)-5 b(able)31 b(in)g(P)-8 b(A)q(.)76 b(Indeed,)31 b(Kreisel)h([32)q(])g(sho)m(w)m(ed)g(the)g(follo)m(wing)h (\(see)0 2150 y(also)e([6)q(]\).)0 2363 y Fi(Lemma)k(3)g(\(Kreisel\))45 b Fq(A)37 b(function)i(is)f(pr)-5 b(ovably)40 b(r)-5 b(e)g(cursive)38 b(in)g FD(P)-8 b(A)16 b(+\005)2619 2377 y Fy(1)2696 2363 y Fq(if)38 b(and)h(only)g(if)f(it's)g(pr)-5 b(ovably)40 b(r)-5 b(e-)0 2476 y(cursive)32 b(in)h FD(P)-8 b(A)p Fq(.)141 2688 y FD(No)m(w)37 b(supp)s(ose)f FC(P)g FD(vs.)h FC(NP)g FD(w)m(ere)g(indep)s(enden)m(t)e(of)i(P)-8 b(A)16 b(+\005)2226 2702 y Fy(1)2265 2688 y FD(.)96 b(Then)35 b FC(NP)i FD(w)m(ould)g(need)f(to)i(ha)m(v)m(e)f(circuits)0 2801 y(of)d(size)h Fp(n)338 2768 y Fy(log)12 b Fo(n)487 2801 y FD(|for)34 b(if)f(it)i(didn't,)f(then)f(w)m(e'd)h(ha)m(v)m(e)h (a)f(true)g(\005)2178 2815 y Fy(1)2218 2801 y FD(-sen)m(tence)h(\(and)f (hence)g(theorem)g(of)g(P)-8 b(A)15 b(+\005)3825 2815 y Fy(1)3865 2801 y FD(\))0 2914 y(that)36 b(implies)g FC(P)e Fn(6)p FD(=)g FC(NP)p FD(.)72 b(Indeed,)36 b(b)m(y)g(Kreisel's)g (lemma,)h FC(NP)g FD(w)m(ould)e(need)g(to)i(ha)m(v)m(e)g(circuits)f(of) g(size)g Fp(n)3728 2881 y Fo(\013)p Fy(\()p Fo(n)p Fy(\))3875 2914 y FD(,)0 3027 y(where)d Fp(\013)h FD(is)f(an)m(y)h(un)m(b)s (ounded)d(function)i(suc)m(h)g(that)h Fp(\013)1925 2994 y Ff(\000)p Fy(1)2053 3027 y FD(is)g(pro)m(v)-5 b(ably)33 b(recursiv)m(e)h(in)f(P)-8 b(A)q(.)83 b(F)-8 b(or)34 b(example,)h(w)m(e)0 3140 y(could)f(tak)m(e)i Fp(\013)e FD(to)h(b)s(e)f(the)g(in)m(v)m(erse)h(Ac)m(k)m(ermann)g(function.)85 b(One)34 b(can)g(obtain)h(ridiculous)e(consequences)i(for)0 3253 y(uniform)c(computation)i(also|although)h(there,)f(to)g(k)m(eep)g (the)g(sen)m(tences)g(\005)2707 3267 y Fy(1)2747 3253 y FD(,)g(one)f(needs)g(to)h(sa)m(y)g(something)0 3366 y(lik)m(e,)e(\\there)f(exists)f(in)g(algorithm)h(that)g(decides)f(SA)-8 b(T)29 b(in)g(time)h Fp(n)2315 3333 y Fo(\013)p Fy(\()p Fo(n)p Fy(\))2491 3366 y FD(for)f(in\014nitely)g(man)m(y)g(long)h (stretc)m(hes)g(of)0 3479 y Fp(n)p FD('s.")0 3765 y FE(6)135 b(Conclusion)0 3968 y FD(It's)36 b(clear)i(that)f(a)f(pro)s(of)g(of)g FC(P)f Fn(6)p FD(=)g FC(NP)p FD(,)j(if)e(it)h(exists)g(at)g(all,)g(w)m (ould)f(require)g(utterly)h(new)e(tec)m(hniques.)95 b(The)0 4081 y(results)32 b(of)g(the)g(previous)g(section)h(t)m(wist)g(the)f (knife)g(further)f(b)m(y)h(sho)m(wing)g(that,)h(if)f FC(P)c Fn(6)p FD(=)g FC(NP)33 b FD(is)f(unpro)m(v)-5 b(able)31 b(in)0 4194 y(a)h(strong)f(theory)h(suc)m(h)f(as)h(P)m(eano)g (arithmetic,)h(then)f(utterly)f(new)g(tec)m(hniques)h(w)m(ould)g(b)s(e) e(required)h(to)h(sho)m(w)0 4307 y Fq(that)p FD(.)80 b(These)33 b(p)s(essimistic)f(results)g(raise)h(a)g(disturbing)e(p)s (ossibilit)m(y:)45 b(could)33 b FC(P)c Fn(6)p FD(=)f FC(NP)33 b FD(b)s(e)f(someho)m(w)h(\\neither)0 4420 y(true)d(nor)g (false?")141 4533 y(Before)39 b(y)m(ou)g(dismiss)e(this)h(question)g (as)h(silly)-8 b(,)41 b(consider)d(the)g(case)h(of)g(the)f(con)m(tin)m (uum)g(h)m(yp)s(othesis)g(CH.)0 4645 y(Unlik)m(e)33 b(G\177)-45 b(odel's)33 b(Incompleteness)g(Theorem,)f(whic)m(h)g(tells)i(us)d(that) i(a)f(sen)m(tence)i(is)e(true)g(b)m(y)g(the)g(v)m(ery)h(fact)g(of)0 4758 y(its)e(unpro)m(v)-5 b(abilit)m(y)d(,)32 b(the)f(indep)s(endence)f (results)h(of)g(G\177)-45 b(odel)31 b(and)g(Cohen)f(don't)h(p)s(oin)m (t)g(us)f(one)h(w)m(a)m(y)h(or)f(another)0 4871 y(regarding)e(the)g (\\truth")g(of)g(CH.)69 b(Can)m(tor)29 b(though)m(t)h(CH)e(w)m(as)i (true.)68 b(G\177)-45 b(odel)30 b(hop)s(ed)e(that)h(new)g (\\self-eviden)m(t")0 4984 y(axioms)39 b(w)m(ould)g(someda)m(y)g(b)s(e) f(disco)m(v)m(ered,)k(whic)m(h)d(w)m(ould)f(settle)i(once)f(and)f(for)h (all)g(whether)f(in)m(termediate)0 5097 y(cardinalities)24 b(exist.)62 b(Cohen)22 b(predicted)h(that)h(CH)e(migh)m(t)i(come)f(to)h (b)s(e)e(seen)h(as)g Fq(obviously)32 b FD(false|a)24 b(prediction)0 5210 y(that's)30 b(partly)g(come)h(to)f(pass)g(\(see,)h (for)e(example,)i(a)f(surv)m(ey)g(b)m(y)f(W)-8 b(o)s(o)s(din)30 b([62)q(]\).)71 b(But)30 b(ev)m(en)g(if)g(w)m(e)g(reject)h(CH,)0 5323 y(there)40 b(remains)g(the)h(question:)60 b(ho)m(w)40 b(man)m(y)h(in)m(termediate)g(cardinalities)h(are)f(there?)110 b(It)40 b(turns)f(out)h(that)p eop end %%Page: 17 17 TeXDict begin 17 16 bop 0 91 a Fq(any)42 b FD(n)m(um)m(b)s(er)32 b(w)m(ould)h(b)s(e)g(consisten)m(t)h(with)f(ZF.)83 b(Cohen)33 b(though)m(t)h(p)s(erhaps)d(there)j(are)f(uncoun)m(tably)h(man)m(y;)0 204 y(W)-8 b(o)s(o)s(din)30 b(thinks)g(there's)h(exactly)h(one.)141 317 y(Should)22 b(w)m(e)i(lose)g(sleep)g(o)m(v)m(er)h(this)e (situation?)63 b(My)23 b(o)m(wn)h(feeling)g(is)g(that)g(w)m(e)g (shouldn't|but)e(that)i(p)s(erhaps)0 430 y(w)m(e)34 b Fq(should)45 b FD(readjust)34 b(our)f(in)m(tuitions)i(regarding)f(the)g (con)m(tin)m(uum.)86 b(Y)-8 b(ou)35 b(migh)m(t)f(think)g(y)m(ou)g(kno)m (w)g(what)g(an)0 543 y(\\arbitrary)23 b(set)h(of)f(reals")h(means,)h (but)e(do)g(y)m(ou?)61 b(Imagine)24 b(y)m(ou)f(w)m(ere)h(a)f (programmer,)i(and)d(y)m(our)h(b)s(oss)g(ordered)0 656 y(y)m(ou)29 b(to)f(write)h(a)f(C)g(program)g(that)h(lo)s(ops)f(through) g(all)h(sets)f(of)h(reals,)g(halting)g(if)f(it)h(\014nds)d(one)j(of)f (in)m(termediate)0 769 y(cardinalit)m(y)-8 b(.)69 b(Y)-8 b(ou)28 b(migh)m(t)g(b)s(e)f(forgiv)m(en)h(for)f(protesting,)i(with)e (Kronec)m(k)m(er,)j(that)e(\\Go)s(d)f(created)i(the)e(in)m(tegers;)0 882 y(all)k(else)g(is)g(the)f(w)m(ork)h(of)f(Man.")141 995 y(Da)m(vid)38 b(Deutsc)m(h,)h(of)e(quan)m(tum)f(computing)h(fame,)i (has)d(argued)h(that)g(ev)m(en)g(mathematical)i(statemen)m(ts)0 1108 y(are)d(ultimately)g(ab)s(out)f(ph)m(ysical)h(realit)m(y|since)h (mathematics)g(is)e(ro)s(oted)g(in)g(computation,)i(and)e(the)g(la)m (ws)0 1220 y(of)d(ph)m(ysics)g(determine)g(what)f(is)h(and)g(isn't)g (computable)g([16)q(].)2208 1187 y Fy(13)2360 1220 y FD(Whether)g(or)g(not)g(y)m(ou)g(agree)h(with)f(this,)g(it)0 1333 y(do)s(es)e(suggest)h(the)g(follo)m(wing)h(\\ph)m(ysical)f(pro)s (cess)f(criterion")i(for)e(mathematical)i(truth:)227 1529 y Fq(We)i(should)i(exp)-5 b(e)g(ct)36 b(a)f(mathematic)-5 b(al)37 b(question)e(to)g(have)g(a)g(de\014nite)f(answer,)i(if)f(and)g (only)g(if)g(we)227 1642 y(c)-5 b(an)34 b(phr)-5 b(ase)34 b(the)f(question)g(in)f(terms)i(of)f(a)g(physic)-5 b(al)34 b(pr)-5 b(o)g(c)g(ess)35 b(we)e(c)-5 b(an)33 b(imagine.)141 1837 y FD(There)d(migh)m(t)i(b)s(e)e(questions)g(that)i(w)m(e)f(can't)g (phrase)f(in)g(terms)h(of)g(a)g(ph)m(ysical)g(pro)s(cess,)f(but)g(that) i(w)m(e)f(can)0 1950 y(nev)m(ertheless)g(answ)m(er|for)e(example,)i (whether)e Fn(j)q Fp(S)5 b Fn(j)25 b Fp(<)1968 1873 y Fb(\014)1968 1927 y(\014)1998 1950 y FD(2)2043 1917 y Fo(S)2095 1873 y Fb(\014)2095 1927 y(\014)2155 1950 y FD(for)k(ev)m(ery)i(set)g Fp(S)5 b FD(.)70 b(Someone)30 b(who)g(accepted)h(the)0 2063 y(ph)m(ysical)39 b(pro)s(cess)f (criterion)i(w)m(ould)e(see)h(these)g(cases)h(as)e(fortuitous)h (acciden)m(ts|and)g(w)m(ould)g(predict)f(that)0 2176 y(closely)32 b(related)f(questions)g(can)f(b)s(e)g(found)f(whic)m(h)h (are)h(unansw)m(erable.)141 2289 y(That)36 b(brings)f(us)h(to)g FC(P)g FD(vs.)g FC(NP)q FD(.)93 b(I'v)m(e)37 b(argued)f(that,)i(lik)m (e)g(the)e(Con)m(tin)m(uum)f(Hyp)s(othesis,)j FC(P)d Fn(6)p FD(=)f FC(NP)i FD(is)h(a)0 2402 y(statemen)m(t)h(as)d(m)m(uc)m (h)h(ab)s(out)f(as)h(of)g(mathematics|one)i(whose)d(truth)g(or)h (falseho)s(o)s(d)f(is)h(almost)g(imp)s(ossible)0 2514 y(to)h(in)m(v)m(estigate)i(without)d(also)h(in)m(v)m(estigating)i(the)e (means)f(of)g(in)m(v)m(estigation.)97 b(But)36 b(in)g(one)h(crucial)g (resp)s(ect,)0 2627 y FC(P)g Fn(6)p FD(=)g FC(NP)h FD(is)f(not)h(at)g (all)h(lik)m(e)g(CH)o(.)100 b(It's)37 b(a)h(\005)1631 2641 y Fy(2)1671 2627 y FD(-sen)m(tence.)101 b(It)38 b(refers,)h(not)e(to)i(a)f(trans\014nite)f(realm)h(b)s(ey)m(ond)0 2740 y(h)m(uman)30 b(exp)s(erience,)g(but)g(to)h(mac)m(hines,)g(Bo)s (olean)h(circuits,)f(1's)g(and)f(0's.)141 2853 y(Here's)g(a)f(simple)h (argumen)m(t)f(for)g(wh)m(y)-8 b(,)30 b(if)f(y)m(ou)g(accept)i(the)e (ph)m(ysical)h(pro)s(cess)e(criterion,)j(then)d(y)m(ou)i(should)0 2966 y(accept)k(that)e(an)m(y)h(\005)725 2980 y Fo(\013)774 2966 y FD(-sen)m(tence)h(has)e(a)h(de\014nite)f(truth-v)-5 b(alue,)32 b(where)g Fp(\013)h FD(is)f(a)g(coun)m(table)i(ordinal.)78 b(Think)31 b(of)0 3079 y(in)m(teractiv)m(e)k(pro)s(ofs.)79 b(Na)-10 b(\177)-35 b(\020v)m(ely)-8 b(,)36 b(one)d(migh)m(t)g(sa)m(y)g (that)g(whether)f(a)h(language)h(b)s(elongs)f(to)g FC(PSP)-8 b(A)m(CE)33 b FD(or)g FC(NEXP)0 3192 y FD(is)c(irrelev)-5 b(an)m(t,)30 b(since)g(those)f(classes)h(lie)g(so)f(far)f(b)s(ey)m(ond) g(what)h(w)m(e)g(could)g(compute)g(or)g(ev)m(en)h(v)m(erify)-8 b(.)70 b(But)29 b(if)f(w)m(e)0 3305 y(p)s(ostulate)33 b(a)g Fq(pr)-5 b(over)44 b FD(who)32 b(can)h(in)m(teract)h(with)f (us|or)e(m)m(ultiple)j(pro)m(v)m(ers,)f(or)g(a)g(probabilistically-c)m (hec)m(k)-5 b(able)0 3418 y(pro)s(of|then)44 b(these)h(questions)f(b)s (ecome)h(relev)-5 b(an)m(t.)129 b(Analogously)-8 b(,)51 b(although)45 b(a)f(\005)3086 3432 y Fy(2)3126 3418 y FD(-sen)m(tence)i(migh)m(t)g(b)s(e)0 3531 y(b)s(ey)m(ond)31 b(our)f(capacit)m(y)k(to)e(v)m(erify)f(if)g(true)g(or)h(falsify)f(if)g (false)h(in)f(an)m(y)h(\014nite)f(amoun)m(t)h(of)f(time,)h(that)g(no)f (longer)0 3644 y(holds)40 b(if)h(w)m(e)f(ha)m(v)m(e)i(an)f(omniscien)m (t)g(wizard)g(around.)110 b(W)-8 b(e)42 b(prop)s(ose)e(an)g(e\016cien)m (t)i(algorithm,)i(the)d(wizard)0 3756 y(resp)s(onds)25 b(with)h(a)h(SA)-8 b(T)26 b(instance)i(on)e(whic)m(h)h(it)g(fails,)h(w) m(e)f(prop)s(ose)f(another)h(algorithm,)i(the)d(wizard)h(resp)s(onds)0 3869 y(with)j(another)h(instance,)g(etc.)72 b(This)30 b(pro)s(cess)g(will)g(con)m(tin)m(ue)i(forev)m(er)f(if)f(and)g(only)h (if)f FC(P)25 b Fn(6)p FD(=)g FC(NP)q FD(.)141 3982 y(The)h(same)g (argumen)m(t)h(w)m(orks)f(for)g(a)h(\005)1479 3996 y Fy(3)1518 3982 y FD(-sen)m(tence,)i Fn(8)p Fp(x)p Fn(9)p Fp(y)s Fn(8)p Fp(z)g(P)f FD(\()p Fp(x;)15 b(y)s(;)g(z)t FD(\))r(.)65 b(W)-8 b(e)27 b(just)f(need)g(to)h(do)m(v)m(etail.)68 b(W)-8 b(e)0 4095 y(prop)s(ose)30 b Fp(x)389 4109 y Fy(1)428 4095 y FD(,)h(the)g(wizard)f(resp)s(onds)f(with)h Fp(y)1564 4109 y Fy(1)1603 4095 y FD(,)h(w)m(e)g(c)m(hec)m(k)h Fp(P)c FD(\()p Fp(x)2211 4109 y Fy(1)2251 4095 y Fp(;)15 b(y)2336 4109 y Fy(1)2375 4095 y Fp(;)g(z)t FD(\))31 b(for)g(the)f(\014rst)g(few)h(v)-5 b(alues)30 b(of)h Fp(z)t FD(.)72 b(Then)0 4208 y(w)m(e)33 b(prop)s(ose)e Fp(x)526 4222 y Fy(2)566 4208 y FD(,)i(the)f(wizard)g(resp)s(onds)e (with)i Fp(y)1710 4222 y Fy(2)1749 4208 y FD(,)h(w)m(e)g(c)m(hec)m(k)h Fp(P)28 b FD(\()p Fp(x)2363 4222 y Fy(2)2403 4208 y Fp(;)15 b(y)2488 4222 y Fy(2)2527 4208 y Fp(;)g(z)t FD(\))33 b(for)f(the)h(\014rst)e(few)h(v)-5 b(alues)33 b(of)f Fp(z)t FD(,)i(as)0 4321 y(w)m(ell)i(as)f Fp(P)29 b FD(\()p Fp(x)479 4335 y Fy(1)518 4321 y Fp(;)15 b(y)603 4335 y Fy(1)643 4321 y Fp(;)g(z)t FD(\))36 b(for)f(a)g(few)g(more)g(v)-5 b(alues)36 b(of)f Fp(z)t FD(.)90 b(And)34 b(so)i(on.)90 b(It's)35 b(not)g(hard)f(to)i(sho)m(w)f(b)m(y)g(induction)0 4434 y(that,)28 b(for)f(an)m(y)h(\005)592 4448 y Fo(\013)641 4434 y FD(-sen)m(tence)h Fp(A)e FD(\(where)g Fp(\013)g FD(is)g(a)g(coun)m(table)h(ordinal\),)h(there)e(exists)g(an)g(\\in)m (teractiv)m(e)k(proto)s(col")0 4547 y(that)g(con)m(tin)m(ues)g(forev)m (er)g(if)g(and)f(only)g(if)g Fp(A)h FD(is)f(true.)141 4660 y(It)d(migh)m(t)g(b)s(e)e(ob)5 b(jected)27 b(that)g(an)g (omniscien)m(t)g(wizard)f(do)s(esn't)g(corresp)s(ond)f(to)i(a)g(ph)m (ysical)g(pro)s(cess)f(w)m(e)h(can)0 4773 y(imagine.)86 b(But)35 b(pro)m(vided)e(w)m(e)i(can)f(imagine)h(pla)m(ying)g(the)f (game)h(against)g(an)f(opp)s(onen)m(t)g(with)f(an)h(arbitrary)0 4886 y(\014xed)39 b(strategy)-8 b(,)45 b(it)40 b(seems)g(legitimate)j (also|at)f(least)f(to)f(me!|to)h(imagine)g(that)g(the)f(opp)s(onen)m(t) g(uses)f(an)0 4998 y Fq(optimal)j FD(strategy)-8 b(.)p 0 5072 1560 4 v 73 5126 a Fu(13)138 5157 y Ft(Most)30 b(computer)f(scien)n(tists)h(w)n(ould)g(agree)g(that)f(the)g (\\extended")f(\(or)i(p)r(olynomial-time\))g(Ch)n(urc)n(h-T)-6 b(uring)28 b(thesis)i(dep)r(ends)0 5249 y(on)c(ph)n(ysical)h(la)n(ws,)h (and)e(indeed)h(is)g(probably)f(falsi\014ed)h(b)n(y)f(quan)n(tum)f(mec) n(hanics.)64 b(Deutsc)n(h,)26 b(ho)n(w)n(ev)n(er,)h(go)r(es)h(further,) e(and)h(sa)n(ys)0 5340 y(that)e(under)g(di\013eren)n(t)g(la)n(ws)i(of)g (ph)n(ysics,)e(ev)n(en)g(the)h(set)g(of)g(computable)g(functions)g(w)n (ould)g(in)g(general)g(b)r(e)g(di\013eren)n(t.)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 141 91 a FD(If)31 b(y)m(ou're)h(still)h (reading)e(this,)h(p)s(erhaps)e(y)m(ou'v)m(e)j(really)f(gotten)h(in)m (to)g(the)e(spirit)h(of)f(it)h(and)f(ask)m(ed:)44 b(what)31 b(if)0 204 y(the)36 b(univ)m(erse)g(is)f(\014nite?)92 b(Recen)m(t)37 b(evidence)g(for)e(a)i(p)s(ositiv)m(e)f(cosmological)j (constan)m(t)e(\(e.g.)58 b([43)r(]\),)37 b(together)0 317 y(with)k(argumen)m(ts)g(from)g(blac)m(k)h(hole)g(thermo)s(dynamics) e([7)q(],)45 b(imply)40 b(an)h(upp)s(er)f(b)s(ound)f(of)i(ab)s(out)g (10)3652 284 y Fy(122)3804 317 y FD(on)0 430 y(the)35 b(maxim)m(um)g(n)m(um)m(b)s(er)f(of)h(bits)g(accessible)i(b)m(y)e(an)m (y)g(one)h(observ)m(er.)89 b(In)m(tuitiv)m(ely)-8 b(,)39 b(ev)m(en)d(if)f(the)g(univ)m(erse)g(is)0 543 y(spatially)30 b(in\014nite,)f(most)g(of)g(it)h(recedes)f(to)s(o)h(quic)m(kly)f(from)f (an)m(y)i(one)f(observ)m(er)g(to)g(b)s(e)f(seen)h(b)m(y)g(that)g (observ)m(er.)0 656 y(No)m(w,)e(what)d(if)g(y)m(our)h(con)m(v)m (ersation)h(with)e(the)h(wizard)f(w)m(ould)g(terminate)i(ev)m(en)m (tually)g(in)e(a)h(pro)s(of)f(that)h FC(P)g FD(=)g FC(NP)q FD(,)0 769 y(but)j(only)h(after)g(y)m(ou'd)f(exc)m(hanged)i(strings)e (m)m(uc)m(h)h(longer)g(than)f(10)2363 736 y Fy(122)2503 769 y FD(bits?)68 b(W)-8 b(ould)29 b(the)g(con)m(v)m(ersation)h(then)0 882 y(satisfy)g(the)f(ph)m(ysical)h(pro)s(cess)e(criterion)i(or)g(not?) 69 b(I'll)30 b(lea)m(v)m(e)h(the)e(answ)m(er)g(to)h(this)f(as)h(a)f (matter)h(of)g(taste.)70 b(I'll)0 995 y(sa)m(y)33 b(only)g(that)f(m)m (y)h(o)m(wn)f(\\Platonic)j(circle"|that)f(is,)f(the)g(set)g(of)f (mathematical)j(en)m(tities)f(that)f(I'm)f(willing)0 1108 y(to)26 b(regard)f(as)h(ph)m(ysically)g(imaginable|do)s(esn't)g (extend)g(all)g(the)f(w)m(a)m(y)h(to)g(uncoun)m(table)g(in\014nities,)g (but)f(it)h Fq(do)-5 b(es)0 1220 y FD(extend)30 b(to)i(in)m(tegers)f (past)g(10)1031 1187 y Fy(122)1142 1220 y FD(,)f(and)g(ev)m(en)h(2)1626 1187 y Fy(10)1696 1164 y Fu(122)1797 1220 y FD(.)141 1333 y(So)g(I'll)g(state,)h(as)f(one)h(of)e(the)h(few)g(de\014nite)f (conclusions)i(of)e(this)h(surv)m(ey)-8 b(,)31 b(that)h FC(P)26 b Fn(6)p FD(=)f FC(NP)31 b FD(is)g(either)g(true)g(or)0 1446 y(false.)71 b(It's)30 b(one)g(or)g(the)g(other.)70 b(But)30 b(w)m(e)g(ma)m(y)h(not)f(b)s(e)f(able)h(to)h(pro)m(v)m(e)g (whic)m(h)e(w)m(a)m(y)i(it)f(go)s(es,)h(and)e(w)m(e)h(ma)m(y)h(not)0 1559 y(b)s(e)f(able)h(to)g(pro)m(v)m(e)g(that)g(w)m(e)g(can't)g(pro)m (v)m(e)g(it.)0 1846 y FE(7)135 b(F)-11 b(urther)44 b(Reading)0 2049 y FD(F)-8 b(or)31 b(the)g(curren)m(t)f(consensus)g(on)g FC(P)g FD(vs.)h FC(NP)p FD(,)g(see)g(William)h(Gasarc)m(h's)f(\\)p FC(P)p FD(=?)p FC(NP)g FD(p)s(oll")g([19)q(]|or)f(go)i(to)844 2253 y(h)m(ttp://www.ideosphere.com/fx-bin/Claim?claim=P!NP)0 2457 y(to)f(b)s(et)f(on)g(whether)g FC(P)c Fn(6)p FD(=)e FC(NP)31 b FD(will)g(b)s(e)f(pro)m(v)m(ed)g(b)m(y)h(2010.)72 b(See)31 b(m)m(y)g(Complexit)m(y)g(Zo)s(o)f(at)985 2661 y(h)m(ttp://www.cs.b)s(erk)m(eley)-8 b(.edu/~aaronson/zo)s(o.h)m(tml)0 2865 y(for)39 b(more)h(ab)s(out)g(the)g(complexit)m(y)h(classes)g(men)m (tioned)f(in)f(this)h(surv)m(ey)-8 b(.)108 b(My)40 b(fa)m(v)m(orite)i (reference)e(for)g(the)0 2978 y(material)h(of)f(Section)h(2)f(is)g(the) g(b)s(o)s(ok)f(of)h(Cohen)f([13)q(].)109 b(F)-8 b(or)41 b(a)f(de\014nition)g(of)g(Cutting)f(Planes)h(and)g(other)0 3091 y(pro)s(of)35 b(systems)h(men)m(tioned)h(in)e(Section)i(4.1,)i (see)e(the)f(surv)m(ey)g(of)g(Beame)h(and)e(Pitassi)i([5)q(].)94 b(Finally)-8 b(,)39 b(there)0 3204 y(are)29 b(in)m(teresting)h (discussions)d(ab)s(out)h(the)h(logical)i(status)d(of)h FC(P)f FD(vs.)h FC(NP)g FD(on)f(the)g(F)-8 b(oundations)29 b(of)g(Mathematics)0 3317 y(\(F)m(OM\))j(mailing)f(list;)g(see)632 3521 y(h)m(ttp://www.cs.n)m(yu.edu/pip)s(ermail/fom/2001-August/005045) q(.h)m(tml.)0 3808 y FE(8)135 b(Ac)l(kno)l(wledgmen)l(ts)0 4011 y FD(I)27 b(thank)f(Lance)i(F)-8 b(ortno)m(w)28 b(and)e(Alexander)i(Razb)s(oro)m(v)f(for)g(their)g(commen)m(ts)h(\(ev)m (en)g(though)f(they)g(don't)g(agree)0 4124 y(with)j(ev)m(erything)h(I)f (sa)m(y)h(here!\).)0 4410 y FE(References)45 4613 y FD([1])47 b(M.)31 b(Agra)m(w)m(al,)h(N.)f(Ka)m(y)m(al,)h(and)e(N.)h(Saxena.)61 b(Primes)30 b(is)h(in)f(P)-8 b(,)30 b(submitted,)h(2002.)187 4726 y(www.cse.iitk.ac.in/users/manindra/primalit)m(y)-8 b(.ps.)45 4914 y([2])47 b(M.)31 b(Ajtai.)62 b(\006)680 4881 y Fy(1)680 4938 y(1)749 4914 y FD(form)m(ulae)31 b(on)f(\014nite)h(structures,)f Fq(A)n(nnals)i(of)h(Pur)-5 b(e)33 b(and)g(Applie)-5 b(d)34 b(L)-5 b(o)g(gic)36 b FD(24:1{48,)e(1983.)45 5101 y([3])47 b(L.)30 b(Babai,)h(L.)f(F)-8 b(ortno)m(w,)31 b(and)e(C.)h(Lund.)58 b(Nondeterministic)30 b(exp)s(onen)m(tial)h(time)g(has)e(t)m(w)m(o-pro)m(v)m(er)j(in)m(ter-) 187 5214 y(activ)m(e)g(proto)s(cols,)g Fq(Computational)k(Complexity)k FD(1\(1\):3{40,)34 b(1991.)187 5327 y (www.neci.nec.com/homepages/fortno)m(w/pap)s(ers/mip2.ps.)p eop end %%Page: 19 19 TeXDict begin 19 18 bop 45 91 a FD([4])47 b(T.)33 b(P)-8 b(.)33 b(Bak)m(er,)i(J.)e(Gill,)i(and)e(R.)g(Solo)m(v)-5 b(a)m(y)d(.)68 b(Relativizations)37 b(of)c(the)g(P=?NP)f(question,)j Fq(SIAM)f(Journal)187 204 y(on)f(Computing)39 b FD(4\(4\):431{442,)d (1975.)45 391 y([5])47 b(P)-8 b(.)104 b(Beame)i(and)d(T.)h(Pitassi.)209 b(Prop)s(ositional)105 b(pro)s(of)e(complexit)m(y:)190 b(past,)123 b(presen)m(t,)187 504 y(and)144 b(future,)173 b Fq(Bul)5 b(letin)138 b(of)g(the)h(EA)-7 b(TCS)155 b FD(65:66{89,)177 b(June)144 b(1998.)292 b(exter-)187 617 y(nal.nj.nec.com/homepages/fortno)m(w/b)s(eatcs/column65.ps.)45 804 y([6])47 b(S.)34 b(Ben-Da)m(vid)j(and)d(S.)g(Halevi.)72 b(On)34 b(the)h(indep)s(endence)e(of)i(P)g(v)m(ersus)f(NP)-8 b(,)36 b(T)-8 b(ec)m(hnical)36 b(Rep)s(ort)f(#699,)187 917 y(T)-8 b(ec)m(hnion,)31 b(1991.)63 b(www.cs.tec)m (hnion.ac.il/~shai/ph.ps.gz.)45 1104 y([7])47 b(R.)33 b(Bousso.)66 b(P)m(ositiv)m(e)35 b(v)-5 b(acuum)33 b(energy)g(and)f (the)h(N-b)s(ound,)g Fq(J.)h(High)h(Ener)-5 b(gy)35 b(Phys.)e FD(0011:038,)k(2000.)187 1217 y(www.arxiv.org/abs/hep-th/0010252.)45 1404 y([8])47 b(H.)29 b(Buhrman,)e(L.)i(F)-8 b(ortno)m(w,)30 b(and)56 b(Thierauf.)g(Nonrelativizing)30 b(separations,)g(in)e Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)33 b(of)e(IEEE)187 1517 y(Complexity'98)p FD(,)i(pp.)d(8{12,)i(1998.)63 b (www.neci.nec.com/homepages/fortno)m(w/pap)s(ers/nonrel.ps.)45 1704 y([9])47 b(S.)30 b(Buss.)60 b Fq(Bounde)-5 b(d)34 b(A)n(rithmetic)p FD(,)d(Bibliop)s(olis,)h(1986.)0 1891 y([10])47 b(S.)25 b(Buss.)51 b(Bounded)25 b(arithmetic)h(and)f(prop)s (ositional)h(pro)s(of)f(complexit)m(y)-8 b(,)29 b(in)c Fq(L)-5 b(o)g(gic)29 b(of)f(Computation)35 b FD(\(H.)187 2004 y(Sc)m(h)m(wic)m(h)m(ten)m(b)s(erg,)d(ed.\),)f(pp.)e(67{122,)34 b(Springer-V)-8 b(erlag,)31 b(1997.)187 2117 y (math.ucsd.edu/~sbuss/Researc)m(hW)-8 b(eb/marktob)s(erdorf95/index.h)m (tml.)0 2304 y([11])47 b(S.)30 b(Buss.)60 b(Bounded)30 b(arithmetic,)i(cryptograph)m(y)-8 b(,)31 b(and)f(complexit)m(y)-8 b(,)33 b Fq(The)-5 b(oria)39 b FD(63:147{167,)c(1997.)187 2417 y(math.ucsd.edu/~sbuss/Researc)m(hW)-8 b(eb/theoria/index.h)m (tml.)0 2604 y([12])47 b(Cla)m(y)21 b(Math)g(Institute.)41 b(Millennium)20 b(Prize)h(Problems.)40 b(www.cla)m (ymath.org/Millennium)p 3401 2604 28 4 v 35 w(Prize)p 3639 2604 V 33 w(Problems.)0 2791 y([13])47 b(P)-8 b(.)31 b(J.)f(Cohen.)60 b Fq(Set)33 b(The)-5 b(ory)34 b(and)g(the)f(Continuum) g(Hyp)-5 b(othesis)p FD(,)32 b(Addison-W)-8 b(esley)g(,)33 b(1966.)0 2979 y([14])47 b(S.)25 b(A.)g(Co)s(ok.)50 b(The)25 b(complexit)m(y)h(of)f(theorem-pro)m(ving)h(pro)s(cedures,)f(in)g Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)30 b(of)e(A)n(CM)e(STOC'71)p FD(,)187 3091 y(pp.)j(151{158,)34 b(1971.)0 3279 y([15])47 b(R.)c(E.)h(DeMillo)h(and)e(R.)g(J.)g(Lipton.)87 b(The)43 b(consistency)h(of)f(P=NP)g(and)g(related)h(problems)e(within)187 3392 y(fragmen)m(ts)31 b(of)f(n)m(um)m(b)s(er)f(theory)-8 b(,)32 b(in)e Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)34 b(of)f(A)n(CM)f (STOC'79)p FD(,)f(pp.)e(153{159,)34 b(1979.)0 3579 y([16])47 b(D.)31 b(Deutsc)m(h.)62 b Fq(The)33 b(F)-7 b(abric)33 b(of)g(R)-5 b(e)g(ality)p FD(,)32 b(P)m(enguin,)e(1997.)0 3766 y([17])47 b(A.)31 b(Do)m(xiadis.)62 b Fq(Uncle)32 b(Petr)-5 b(os)34 b(and)f(Goldb)-5 b(ach's)35 b(Conje)-5 b(ctur)g(e)p FD(,)32 b(Blo)s(omsbury)-8 b(,)30 b(2001.)0 3953 y([18])47 b(M.)25 b(F)-8 b(urst,)26 b(J.)e(B.)h(Saxe,)i(and)c(M.)i (Sipser.)49 b(P)m(arit)m(y)-8 b(,)27 b(circuits,)g(and)d(the)h(p)s (olynomial)f(time)i(hierarc)m(h)m(y)-8 b(,)26 b Fq(Math.)187 4066 y(Systems)33 b(The)-5 b(ory)40 b FD(17:13{27,)34 b(1984.)0 4253 y([19])47 b(W.)184 b(Gasarc)m(h.)369 b(The)184 b(P=?NP)f(p)s(oll,)223 b Fq(SIGA)n(CT)173 b(News)192 b FD(36,)223 b(2002.)187 4366 y(www.cs.umd.edu/users/gasarc)m(h/pap)s (ers/p)s(oll.ps.)0 4553 y([20])47 b(K.)g(G\177)-45 b(odel.)96 b Fq(The)48 b(Consistency)h(of)g(the)f(Axiom)h(of)f(Choic)-5 b(e)49 b(and)g(of)g(the)f(Gener)-5 b(alize)g(d)51 b(Continuum-)187 4666 y(Hyp)-5 b(othesis)34 b(with)g(the)f(Axioms)g(of)g(Set)f(The)-5 b(ory)p FD(,)32 b(Princeton)f(Univ)m(ersit)m(y)h(Press,)e(1940.)0 4853 y([21])47 b(O.)38 b(Goldreic)m(h,)k(S.)c(Goldw)m(asser,)j(and)c (S.)h(Micali.)79 b(Ho)m(w)39 b(to)g(construct)g(random)e(functions,)j Fq(J.)f(of)i(the)187 4966 y(A)n(CM)j FD(33:792{807,)35 b(1986.)0 5153 y([22])47 b(R.)30 b(Go)s(o)s(dstein.)61 b(On)30 b(the)g(restricted)i(ordinal)e(theorem,)h Fq(J.)h(of)h(Symb)-5 b(olic)34 b(L)-5 b(o)g(gic)36 b FD(9:33{41,)d(1944.)0 5340 y([23])47 b(A.)31 b(Hak)m(en.)61 b(The)30 b(in)m(tractabilit)m(y)k (of)c(resolution,)h Fq(The)-5 b(or)g(etic)g(al)35 b(Computer)f(Scienc) -5 b(e)37 b FD(39:297{308,)e(1985.)p eop end %%Page: 20 20 TeXDict begin 20 19 bop 0 91 a FD([24])47 b(J.)30 b(Hartmanis.)61 b Fq(F)-7 b(e)i(asible)34 b(Computations)h(and)f(Pr)-5 b(ovable)33 b(Complexity)h(Pr)-5 b(oblems)p FD(,)32 b(SIAM,)f(1978.)0 271 y([25])47 b(J.)27 b(Hartmanis.)55 b(Indep)s(endence)26 b(results)h(ab)s(out)g(con)m(text-free)j(languages)f(and)d(lo)m(w)m(er) j(b)s(ounds,)d Fq(Informa-)187 384 y(tion)33 b(Pr)-5 b(o)g(c.)33 b(L)-5 b(ett.)31 b FD(20\(5\):241{248,)36 b(1985.)0 564 y([26])47 b(J.)c(Hartmanis)h(and)e(J.)h(Hop)s(croft.)87 b(Indep)s(endence)42 b(results)h(in)g(computer)g(science,)48 b Fq(SIGA)n(CT)c(News)187 677 y FD(8\(4\):13{24,)35 b(1976.)0 857 y([27])47 b(J.)84 b(H)-11 b(\027)-57 b(astad,)99 b(R.)85 b(Impagliazzo,)100 b(L.)85 b(Levin,)98 b(and)84 b(M.)h(Lub)m(y)-8 b(.)169 b(A)84 b(pseudorandom)f(gener-)187 970 y(ator)90 b(from)f(an)m(y)g(one-w)m(a)m(y)i(function,)104 b Fq(SIAM)86 b(J.)g(Comput.)k FD(28,)105 b(pp.)89 b(1364{1396,)108 b(1999.)187 1083 y(www.nada.kth.se/~johanh/prgfromo)m(wf.ps.)0 1262 y([28])47 b(D.)d(Joseph)e(and)h(P)-8 b(.)43 b(Y)-8 b(oung.)87 b(Indep)s(endence)42 b(results)h(in)g(computer)g(science?,)k Fq(J.)d(Comp.)i(Sys.)e(Sci.)187 1375 y FD(23:311{338,)35 b(1981.)0 1555 y([29])47 b(R.)37 b(Kannan.)74 b(Circuit-size)38 b(lo)m(w)m(er)h(b)s(ounds)c(and)i(non-reducibilit)m(y)g(to)h(sparse)f (sets,)j Fq(Information)h(and)187 1668 y(Contr)-5 b(ol)42 b FD(55:40{56,)34 b(1982.)0 1848 y([30])47 b(R.)34 b(M.)g(Karp.)67 b(Reducibilit)m(y)35 b(among)f(com)m(binatorial)i(problems,)e(in)g Fq(Complexity)j(of)f(Computer)i(Com-)187 1961 y(putations)h FD(\(R.)31 b(Miller)h(and)d(J.)i(Thatc)m(her,)g(eds.\),)g(Plen)m(um)f (Press,)g(pp.)f(85{104,)34 b(1972.)0 2141 y([31])47 b(J.)27 b(Kra)5 b(j)-10 b(\023)-35 b(\020)m(\024)-43 b(cek)29 b(and)d(P)-8 b(.)28 b(Pudl\023)-45 b(ak.)54 b(Some)27 b(consequences)h(of)f(cryptographical)i(conjectures)e(for)g Fp(S)3491 2108 y Fy(2)3486 2165 y(1)3558 2141 y FD(and)f Fp(E)5 b(F)13 b FD(,)187 2254 y(in)24 b Fq(L)-5 b(o)g(gic)28 b(and)g(Computational)j(Complexity)j FD(\(E.)25 b(D.)g(Levian)m(t,)i (ed.\),)g(Springer)c(LNCS)h(960,)j(pp.)d(210{220,)187 2366 y(1995.)63 b(www.math.cas.cz/~kra)5 b(jicek/j-crypto.ps.gz.)0 2546 y([32])47 b(G.)23 b(Kreisel.)46 b(On)22 b(the)h(concepts)h(of)f (completeness)h(and)e(in)m(terpretation)i(of)f(formal)g(systems,)i Fq(F)-7 b(undamenta)187 2659 y(Mathematic)i(ae)39 b FD(39:103{127,)c (1952.)0 2839 y([33])47 b(S.)30 b(Kurtz,)h(M.)g(J.)g(O'Donnell,)h(and)e (S.)g(Ro)m(y)m(er.)63 b(Ho)m(w)32 b(to)f(pro)m(v)m(e)h(represen)m (tation-indep)s(enden)m(t)f(indep)s(en-)187 2952 y(dence)f(results,)h Fq(Information)k(Pr)-5 b(o)g(c.)33 b(L)-5 b(ett.)31 b FD(24,)g(pp.)f(5{10,)i(Jan)m(uary)e(1987.)0 3132 y([34])47 b(J.)36 b(C.)h(Lagarias.)74 b(An)36 b(elemen)m(tary)i(problem)e(equiv) -5 b(alen)m(t)38 b(to)f(the)g(Riemann)f(h)m(yp)s(othesis,)i(man)m (uscript,)187 3245 y(2000.)63 b(www.arxiv.org/abs/math.NT/0008177.)0 3425 y([35])47 b(A.)31 b(K.)f(Lenstra)h(and)f(H.)h(W.)h(Lenstra)e(Jr.) 61 b Fq(The)33 b(Development)h(of)f(the)g(Numb)-5 b(er)33 b(Field)g(Sieve)p FD(,)e(Springer-)187 3537 y(V)-8 b(erlag,)32 b(1993.)0 3717 y([36])47 b(L.)34 b(Levin.)69 b(Univ)m(ersal)35 b(searc)m(h)f(problems,)h Fq(Pr)-5 b(oblemy)37 b(Per)-5 b(e)g(dachi)38 b(Informatsii)45 b FD(9\(3\):265{266)39 b(\(in)34 b(Rus-)187 3830 y(sian\),)26 b(1973.)50 b(P)m(artial)25 b(English)f(translation)h(in)e(B.)i(A.)f(T)-8 b(rakh)m(ten)m(brot,)26 b(A)e(surv)m(ey)g(of)g(Russion)f(approac)m(hes)187 3943 y(to)31 b Fq(p)-5 b(er)g(eb)g(or)p FD(,)33 b Fq(A)n(nnals)g(of)f(the)h (History)h(of)f(Computing)39 b FD(6\(4\):384{400,)d(1984.)0 4123 y([37])47 b(P)-8 b(.)44 b(B.)h(Miltersen,)j(N.)d(V.)f(Vino)s(dc)m (handran,)j(and)c(O.)h(W)-8 b(atanab)s(e.)89 b(Sup)s(er-p)s(olynomial) 43 b(v)m(ersus)h(half-)187 4236 y(exp)s(onen)m(tial)c(circuit)h(size)f (in)g(the)f(exp)s(onen)m(tial)i(hierarc)m(h)m(y)-8 b(,)43 b(in)d Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)43 b(of)e(COCOON'1999)p FD(,)i(pp.)187 4349 y(210{220,)34 b(1999.)62 b (www.brics.dk/~bromille/P)m(ap)s(ers/co)s(co)s(on.ps.)0 4529 y([38])47 b(R.)30 b(Monk.)61 b Fq(Ludwig)33 b(Wittgenstein:)42 b(The)33 b(Duty)f(of)h(Genius)p FD(,)e(Vin)m(tage,)h(1991.)0 4709 y([39])47 b(K.)81 b(Mulm)m(uley)i(and)e(M.)h(Sohoni.)163 b(Geometric)84 b(complexit)m(y)f(theory)f(I:)g(an)f(approac)m(h)h(to) 187 4821 y(the)93 b(P)g(vs.)g(NP)g(and)g(related)h(problems,)108 b Fq(SIAM)89 b(J.)h(Comput.)k FD(31\(2\):496{526,)115 b(2001.)187 4934 y(h)m(ttp://p)s(eople.cs.uc)m(hicago.edu/~m)m(ulm)m (uley/part1.ps.)0 5114 y([40])47 b(M.)21 b(Naor)g(and)f(O.)g(Reingold.) 42 b(Num)m(b)s(er-theoretic)21 b(constructions)g(of)f(e\016cien)m(t)i (pseudorandom)d(functions,)187 5227 y(in)30 b Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)35 b(of)d(IEEE)g(F)n(OCS'97)p FD(,)f(pp.)f(458{467,)k(1997.)187 5340 y(www.wisdom.w)m (eizmann.ac.il/~naor/P)-8 b(APERS/gdh.ps.)p eop end %%Page: 21 21 TeXDict begin 21 20 bop 0 91 a FD([41])47 b(N.)40 b(Nisan)g(and)f(A.)h (Wigderson.)81 b(Hardness)39 b(vs.)h(randomness,)h Fq(J.)g(Comp.)h (Sys.)g(Sci.)d FD(49\(2\):149{167,)187 204 y(1994.)187 317 y(www.math.ias.edu/~a)m(vi/PUBLICA)-8 b(TIONS/MYP)g(APERS/NO)m (AM/HARDNESS/\014nal.ps.)0 501 y([42])47 b(J.)35 b(P)m(aris)g(and)f(L.) h(Harrington.)70 b(A)35 b(mathematical)i(incompleteness)e(in)g(P)m (eano)h(arithmetic,)h Fq(Handb)-5 b(o)g(ok)187 614 y(of)33 b(Mathematic)-5 b(al)34 b(L)-5 b(o)g(gic)37 b FD(\(J.)30 b(Barwise,)h(ed.\),)h(pp.)d(1133{1142,)35 b(North-Holland,)c(1977.)0 799 y([43])47 b(S.)28 b(P)m(erlm)m(utter)h(and)f(32)h(others)f(\(Sup)s (erno)m(v)-5 b(a)27 b(Cosmology)j(Pro)5 b(ject\).)57 b(Measuremen)m(ts)29 b(of)g(\012)f(and)f(\003)h(from)187 912 y(42)j(high-redshift)f(sup)s(erno)m(v)-5 b(ae,)30 b Fq(Astr)-5 b(ophysic)g(al)35 b(Journal)41 b FD(517\(2\):565{586,)c (1999.)187 1024 y(www.arxiv.org/abs/astro-ph/9812133.)0 1209 y([44])47 b(V.)31 b(R.)f(Pratt.)62 b(Ev)m(ery)30 b(prime)g(has)g(a)h(succinct)g(certi\014cate,)i Fq(SIAM)e(J.)h(Comput.) g FD(4:214{220,)i(1975.)0 1393 y([45])47 b(P)-8 b(.)22 b(Pudl\023)-45 b(ak.)44 b(Lo)m(w)m(er)23 b(b)s(ounds)d(for)i (resolution)h(and)e(cutting)i(planes)f(pro)s(ofs)f(and)h(monotone)h (computations,)187 1506 y Fq(J.)32 b(of)h(Symb)-5 b(olic)34 b(L)-5 b(o)g(gic)36 b FD(62\(3\):981{998,)g(1997.)62 b(www.math.cas.cz/~pudlak/in)m(terp)s(ol.ps.)0 1690 y([46])47 b(R.)35 b(Raz.)72 b FC(P)34 b Fn(6)p FD(=)f FC(NP)q FD(,)k(prop)s (ositional)f(pro)s(of)e(complexit)m(y)-8 b(,)39 b(and)c(resolution)h (lo)m(w)m(er)h(b)s(ounds)c(for)i(the)h(w)m(eak)187 1803 y(pigeonhole)27 b(principle,)g(in)f Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)30 b(of)f(ICM'2002)40 b FD(\(In)m(ternational)28 b(Congress)e(of)g (Mathematicians\),)187 1916 y(V)-8 b(ol.)32 b(I)s(I)s(I,)d(pp.)g (685{693,)34 b(2002.)63 b(www.wisdom.w)m (eizmann.ac.il/~ranraz/publications/Pc)m(hina.ps.)0 2100 y([47])47 b(R.)149 b(Raz.)298 b(Resolution)149 b(lo)m(w)m(er)h(b)s (ounds)c(for)j(the)g(w)m(eak)g(pigeonhole)h(prin-)187 2213 y(ciple,)219 b(in)180 b Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)172 b(of)f(A)n(CM)e(STOC'2002)p FD(,)219 b(pp.)180 b(553{562,)221 b(2002.)187 2326 y(www.wisdom.w)m (eizmann.ac.il/~ranraz/publications/Pwphpres.ps.)0 2511 y([48])47 b(A.)d(A.)g(Razb)s(oro)m(v.)88 b(Bounded)42 b(arithmetic)j(and)e(lo)m(w)m(er)i(b)s(ounds)c(in)i(Bo)s(olean)i (complexit)m(y)-8 b(,)49 b(in)43 b Fq(F)-7 b(e)i(asi-)187 2624 y(ble)41 b(Mathematics)i(II)54 b FD(\(P)-8 b(.)40 b(Clote)h(and)e(J.)h(Remmel,)j(eds.\),)g(Birkh\177)-45 b(auser,)42 b(pp.)d(344{386,)45 b(1995.)82 b(gene-)187 2736 y(sis.mi.ras.ru/~razb)s(oro)m(v/b)s(ob)s(o.ps.)0 2921 y([49])47 b(A.)72 b(A.)g(Razb)s(oro)m(v.)145 b(Lo)m(w)m(er)73 b(b)s(ounds)c(for)j(prop)s(ositional)g(pro)s(ofs)f(and)h(indep)s (endence)e(results)187 3034 y(in)82 b(b)s(ounded)e(arithmetic,)97 b(in)82 b Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)83 b(of)d(ICALP'1996)p FD(,)97 b(pp.)81 b(48{62,)98 b(1996.)167 b(gene-)187 3147 y(sis.mi.ras.ru/~razb)s(oro)m(v/icalp.ps.)0 3331 y([50])47 b(A.)24 b(A.)f(Razb)s(oro)m(v.)48 b(Lo)m(w)m(er)24 b(b)s(ounds)d(for)i(the)g(monotone)h(complexit)m(y)h(of)f(some)g(Bo)s (olean)g(functions,)h Fq(Soviet)187 3444 y(Math.)33 b(Doklady)39 b FD(31:354{357,)c(1985.)0 3628 y([51])47 b(A.)k(A.)g(Razb)s(oro)m(v.) 101 b(Lo)m(w)m(er)52 b(b)s(ounds)c(for)i(the)h(p)s(olynomial)g (calculus,)56 b Fq(Computational)e(Complexity)187 3741 y FD(7\(4\):291{324,)35 b(1988.)63 b(genesis.mi.ras.ru/~razb)s(oro)m (v/p)s(olynom.ps.)0 3925 y([52])47 b(A.)31 b(A.)f(Razb)s(oro)m(v.)62 b(Lo)m(w)m(er)31 b(b)s(ounds)d(on)j(the)f(size)h(of)g(b)s(ounded-depth) d(net)m(w)m(orks)j(o)m(v)m(er)g(a)g(complete)h(basis)187 4038 y(with)e(logical)j(addition,)e Fq(Math.)i(Notes.)f(of)h(the)g(A)-5 b(c)g(ad.)34 b(Sci.)e(of)h(USSR)h FD(41\(4\):333{338,)i(1987.)0 4223 y([53])47 b(A.)23 b(A.)g(Razb)s(oro)m(v.)46 b(Pseudorandom)21 b(generators)j(hard)d(for)i(k-DNF)g(resolution)h(and)d(p)s(olynomial)i (calculus)187 4335 y(resolution,)31 b(man)m(uscript,)f(2003.)63 b(genesis.mi.ras.ru/~razb)s(oro)m(v/res)p 2649 4335 28 4 v 35 w(k.ps.)0 4520 y([54])47 b(A.)40 b(A.)g(Razb)s(oro)m(v.)79 b(Resolution)41 b(lo)m(w)m(er)f(b)s(ounds)e(for)h(p)s(erfect)g(matc)m (hing)i(principles,)g(to)f(app)s(ear)f(in)g Fq(J.)187 4633 y(Comp.)44 b(Sys.)g(Sci.)84 b FD(Preliminary)42 b(v)m(ersion)g(in)g Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)45 b(of)f(IEEE)e(Complexity'2002)p FD(,)49 b(pp.)41 b(29{38,)187 4746 y(2002.)63 b(genesis.mi.ras.ru/~razb)s(oro)m(v/matc)m(hing.ps.)0 4930 y([55])47 b(A.)25 b(A.)g(Razb)s(oro)m(v.)51 b(Unpro)m(v)-5 b(abilit)m(y)25 b(of)g(lo)m(w)m(er)h(b)s(ounds)d(on)i(circuit)g(size)h (in)e(certain)i(fragmen)m(ts)f(of)g(b)s(ounded)187 5043 y(arithmetic,)32 b Fq(Izvestiya)h(Math.)e FD(59\(1\):205{227,)36 b(1995.)0 5227 y([56])47 b(A.)31 b(A.)f(Razb)s(oro)m(v)h(and)f(S.)g (Rudic)m(h.)61 b(Natural)31 b(pro)s(ofs,)f Fq(J.)i(Comp.)h(Sys.)g(Sci.) d FD(55:24{35,)k(1997.)187 5340 y(www-2.cs.cm)m(u.edu/~rudic)m(h/pap)s (ers/natural.ps.)p eop end %%Page: 22 22 TeXDict begin 22 21 bop 0 91 a FD([57])47 b(K.)39 b(W.)h(Regan.)79 b(Understanding)38 b(the)i(Mulm)m(uley-Sohoni)f(approac)m(h)h(to)g(P)f (vs.)g(NP)-8 b(,)40 b Fq(Bul)5 b(letin)41 b(of)g(the)187 204 y(EA)-7 b(TCS)41 b FD(78,)31 b(Octob)s(er)f(2002.)63 b(external.nj.nec.com/homepages/fortno)m(w/b)s(eatcs/column78.ps.)0 392 y([58])47 b(V.)32 b(Y)-8 b(u.)31 b(Sazano)m(v.)64 b(A)31 b(logical)j(approac)m(h)e(to)g(the)f(problem)g(\\P=NP?",)h(in)f Fq(Mathematic)-5 b(al)36 b(F)-7 b(oundations)187 505 y(of)33 b(Computer)h(Scienc)-5 b(e)p FD(,)30 b(Springer)f(LNCS)h(88,)h (pp.)f(562{575,)j(1980.)0 692 y([59])47 b(S.)30 b(Shelah.)60 b(Logical)33 b(dreams,)d(man)m(uscript,)g(2002.)63 b (www.arxiv.org/abs/math.LO/0211398.)0 880 y([60])47 b(M.)e(Sipser.)88 b(The)44 b(history)h(and)f(status)g(of)h(the)g(P)f(v)m(ersus)g(NP)h (question,)j(in)d Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)47 b(of)f(A)n(CM)187 993 y(STOC'92)p FD(,)31 b(pp.)f(603{618,)j(1992.)63 b(www.cs.b)s(erk)m(eley)-8 b(.edu/~luca/cs278/pap)s(ers/sipser.ps.)0 1181 y([61])47 b(R.)23 b(Smolensky)-8 b(.)45 b(Algebraic)24 b(metho)s(ds)e(in)h(the)g(theory)f(of)h(lo)m(w)m(er)h(b)s(ounds)d(for)h (Bo)s(olean)i(circuit)g(complexit)m(y)-8 b(,)187 1293 y(in)30 b Fq(Pr)-5 b(o)g(c)g(e)g(e)g(dings)35 b(of)d(A)n(CM)g(STOC'87)p FD(,)f(pp.)f(77{82,)i(1987.)0 1481 y([62])47 b(H.)36 b(W)-8 b(o)s(o)s(din.)72 b(The)35 b(con)m(tin)m(uum)h(h)m(yp)s (othesis,)h(part)e(I,)h Fq(Notic)-5 b(es)38 b(of)f(the)h(AMS)46 b FD(48\(6\),)39 b(June/July)c(2001.)187 1594 y (www.ams.org/notices/200106/fea-w)m(o)t(o)s(din.p)s(df.)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF