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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 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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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 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 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 0 /.notdef put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 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 0 /.notdef put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 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 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 56 /bracelefttp put
dup 58 /braceleftbt put
dup 60 /braceleftmid put
dup 62 /braceex put
dup 80 /summationtext put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX8
%!PS-AdobeFont-1.1: CMBX8 1.0
%%CreationDate: 1991 Aug 20 16:36:07
% 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 (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX8 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 /.notdef put
readonly def
/FontBBox{-59 -250 1235 750}readonly def
/UniqueID 5000766 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 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 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 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 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
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/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
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end readonly def
/FontName /CMSY8 def
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readonly def
/FontBBox{-30 -955 1185 779}readonly def
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currentdict end
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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 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% 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 (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 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 /.notdef put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% 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 (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 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 /.notdef put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 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 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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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 (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
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/FontName /CMSY7 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
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readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
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4468 y Fj(1)563 4459 y Ft(:::)o(a)659 4467 y Fi(t)688
4459 y Ft(K)748 4467 y Fi(t)775 4344 y Fk(\001)865 4425
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b(an)m(y)h(v)-5 b(ariet)m(y)45 b Fq(V)52 b Fx(of)44 b(languages)g(the)h
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b(e)48 b(of)g Fq(V)8 b Fx(,)51 b(denoted)d Fu(\()p Fq(V)8
b Fu(\))p Fx(,)51 b(is)c(the)g(v)-5 b(ariet)m(y)47 b(generated)h(b)m(y)
g(unam-)257 4666 y(biguous)42 b(concatenations)f(of)g(languages)g(in)g
Fq(V)8 b Fx(.)71 b(Similarly)-8 b(,)39 b(for)i(an)m(y)i(prime)d
Fv(p)p Fx(,)k(the)257 4786 y(Mo)s(d)452 4801 y Ft(p)536
4786 y Fr(p)-5 b(olynomial)43 b(closur)-5 b(e)45 b(of)g
Fq(V)8 b Fx(,)46 b(denoted)f Fu(Mo)s(d)2216 4801 y Ft(p)2256
4786 y Fu(P)m(ol\()p Fq(V)8 b Fu(\))p Fx(,)47 b(is)c(the)h(v)-5
b(ariet)m(y)43 b(gener-)257 4907 y(ated)36 b(b)m(y)g(languages)e(of)h
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4862 y Ft(w)1839 4941 y(K)1899 4950 y Fj(0)1933 4941
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5268 y(pro)s(ducts)c(of)e(pseudo-v)-5 b(arieties)42 b(\(see)h([)1741
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5268 a
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/Dest (cite.Pin97) cvn H.B /ANN pdfmark end
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(pseudo-v)-5 b(ariet)m(y)43 b(of)257 5388 y(monoids)52
b(corresp)s(onding)g(to)h Fq(V)8 b Fx(,)58 b(then)53
b(the)h(pseudo-v)-5 b(arieties)52 b(corresp)s(onding)h(to)p
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/Dest (cite.TessonT05) cvn H.B /ANN pdfmark end
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b(The)37 b(unam)m(biguous)e(p)s(olynomial)e(closure)j(of)257
2678 y(these)k(languages)e(in)f(fact)h(corresp)s(onds)i(to)e(the)h
(pseudo-v)-5 b(ariet)m(y)39 b Fo(DO)26 b Fq(\\)p 3063
2597 147 4 v 26 w Fo(Ab)39 b Fx(whic)m(h)257 2798 y(w)m(e)34
b(discussed)g(earlier.)257 2940 y
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a
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257 3462 y(more)d(pro)s(cessors)i(need)g(to)e(exc)m(hange)j(when)f
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SDict begin H.S end
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3582 a Fx(72)2860 3518 y
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/Dest (cite.Yao79) cvn H.B /ANN pdfmark end
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3582 a Fx(])g(in)g(relation)f(to)257 3703 y(distributed)i(computing)f
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(ortan)m(t)e(connections)j(to)f(VLSI)h(design)257 3944
y(\(see)32 b([)478 3944 y
SDict begin H.S end
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SDict begin H.R end

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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.KN97) cvn H.B /ANN pdfmark end
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(complexit)m(y)h([)2057 3944 y
SDict begin H.S end
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3879 y
SDict begin H.R end
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.Wegener) cvn H.B /ANN pdfmark end
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m(y)h([)3061 3944 y
SDict begin H.S end
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SDict begin H.R end
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3879 a 3158 3944 a
SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.Grolmusz92) cvn H.B /ANN pdfmark end
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SDict begin H.S end
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3944 a Fx(29)3313 3879 y
SDict begin H.R end
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.Grolmusz94b) cvn H.B /ANN pdfmark end
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3944 a Fx(,)3371 3944 y
SDict begin H.S end
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SDict begin H.R end

3468 3879 a 3468 3944 a
SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
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SDict begin H.S end
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4064 a Fx(43)355 4000 y
SDict begin H.R end
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.Nisan94) cvn H.B /ANN pdfmark end
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a Fx(,)409 4064 y
SDict begin H.S end
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SDict begin H.R end
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a 507 4064 a
SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.RazM97) cvn H.B /ANN pdfmark end
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b(uring)27 b(mac)m(hines)g([)2359 4064 y
SDict begin H.S end
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Fx(6)2408 4000 y
SDict begin H.R end
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.BabaiNS92) cvn H.B /ANN pdfmark end
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Fx(],)i(data)e(structures)i([)3186 4064 y
SDict begin H.S end
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Fx(40)3284 4000 y
SDict begin H.R end
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.KN97) cvn H.B /ANN pdfmark end
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Fx(])e(and)257 4184 y(pro)s(of)e(complexit)m(y)f([)1020
4184 y
SDict begin H.S end
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SDict begin H.R end
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4184 a
SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.BeamePS05) cvn H.B /ANN pdfmark end
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SDict begin H.S end
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y
SDict begin H.R end
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.KN97) cvn H.B /ANN pdfmark end
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4305 y(a)33 b(v)m(ery)h(go)s(o)s(d)d(o)m(v)m(erview)j(of)e(the)h
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b(ject.)404 4425 y(In)53 b(a)f(\(v)m(ery)i(en)m(tertaining\))e(pap)s
(er)h([)1843 4425 y
SDict begin H.S end
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SDict begin H.R end
 1892
4361 a 1892 4425 a
SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.BabaiFS86) cvn H.B /ANN pdfmark end
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b(rankl)52 b(and)h(Simon)e(de\034ned)257 4545 y(comm)m(unication)26
b(complexit)m(y)h(analogues)h(of)f(the)i(standard)f(time/space)g
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b(,)26 b(RP)-8 b(,)25 b Fq(\010)p Fx(P)-8 b(,)26 b(PSP)-8
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(under)g(whic)m(h)f(classes)h(lik)m(e)e(NP)-8 b(,)26
b Fq(\010)p Fx(P)h(and)257 4907 y(PSP)-8 b(A)m(CE)40
b(ha)m(v)m(e)f(complete)d(problems.)58 b(This)38 b(pro)m(vides,)h(on)f
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b(extensions)i(of)e(the)h(usual)f(deter-)257 5147 y(ministic)31
b(mo)s(del)h(while)g(building,)f(on)i(the)h(other)f(hand,)h(a)f(ric)m
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SDict begin H.S end
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473 a 257 473 a
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b(a)257 879 y(function)g Fv(f)38 b Fu(:)28 b Fv(X)e Fq(\002)18
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b Fx(while)g(exc)m(hanging)i(as)f(few)h(bits)e(as)h(p)s(ossible.)41
b(The)257 1120 y(t)m(w)m(o)30 b(parties)e(comm)m(unicate)g(according)g
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1241 y(whic)m(h,)34 b(informally)-8 b(,)30 b(is)j(a)g(sc)m(heme)h
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y(eac)m(h)i(other.)53 b(F)-8 b(ormally)g(,)33 b(one)j(usually)f
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b Fx(as)35 b(a)257 1602 y(binary)26 b(tree)h(in)e(whic)m(h)h(edges)i
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b Fv(R)i Fx(and)f(ev)m(ery)i(inner)d(no)s(de)h Fv(s)g
Fx(is)f(either)h(lab)s(eled)e(b)m(y)j(a)f(function)f
Fv(a)2876 1737 y Ft(s)2944 1722 y Fu(:)e Fv(X)39 b Fq(!)31
b(f)p Fu(0)p Fv(;)17 b Fu(1)p Fq(g)257 1843 y Fx(or)41
b(a)f(function)h Fv(b)906 1858 y Ft(s)985 1843 y Fu(:)g
Fv(Y)63 b Fq(!)42 b(f)p Fu(0)p Fv(;)17 b Fu(1)p Fq(g)p
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1536 a
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SDict begin H.S end
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a Fx(11)2050 2314 y
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SDict begin [ /Color [0 1 0] /H /I /Border [0 0 12] /Subtype /Link
/Dest (cite.BarringtonST90) cvn H.B /ANN pdfmark end
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Fz(,)f(30\(6\):1842\025)447 1070 y(1862,)31 b(2000.)257
1092 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.Angluin87a) cvn H.B /DEST
pdfmark end
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1092 a 303 1228 a Fz([4])49 b(D.)33 b(Angluin.)51 b(Learning)35
b(regular)g(sets)e(from)h(queries)f(and)h(coun)m(terexamples.)53
b Fd(Infor-)447 1341 y(mation)31 b(and)i(Computation)p
Fz(,)c(75\(2\):87\025106,)k(1987.)257 1368 y
SDict begin H.S end
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a 257 1368 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BabaiFS86) cvn H.B /DEST
pdfmark end
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a Fz([5])49 b(L.)44 b(Babai,)j(P)-8 b(.)45 b(F)-8 b(rankl,)48
b(and)c(J.)g(Simon.)80 b(Complexit)m(y)45 b(classes)e(in)h(comm)m
(unication)447 1613 y(complexit)m(y)33 b(theory)-8 b(.)47
b(In)31 b Fd(Pr)-5 b(o)g(c.)35 b(27)1670 1580 y Ft(th)1775
1613 y Fd(IEEE)f(Symp.)f(on)g(F)-7 b(oundations)34 b(of)g(Comp.)f(Sci.)
447 1726 y(\(F)n(OCS'86\))p Fz(,)c(pages)h(337\025347,)i(1986.)257
1752 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BabaiNS92) cvn H.B /DEST
pdfmark end
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1752 a 303 1884 a Fz([6])49 b(L.)40 b(Babai,)k(N.)c(Nisan,)j(and)d(M.)g
(Szegedy)-8 b(.)72 b(Multipart)m(y)41 b(proto)s(cols,)i(pseudorandom)
447 1997 y(generators)j(for)f(logspace,)50 b(and)45 b(time-space)h
(trade-o\033s.)85 b Fd(J.)46 b(Comput.)g(Syst.)f(Sci.)p
Fz(,)447 2110 y(45\(2\):204\025232,)32 b(1992.)257 2137
y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.Barrington89) cvn H.B /DEST
pdfmark end
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a 303 2268 a Fz([7])49 b(D.)27 b(A.)g(Barrington.)37
b(Bounded-width)30 b(p)s(olynomial-size)e(branc)m(hing)i(programs)e
(recog-)447 2381 y(nize)36 b(exactly)g(those)g(languages)h(in)f
Fc(N)10 b(C)1881 2348 y Fw(1)1919 2381 y Fz(.)57 b Fd(J.)37
b(Comput.)g(Syst.)f(Sci.)p Fz(,)h(38\(1\):150\025164,)447
2494 y(1989.)k(Preliminary)32 b(v)m(ersion)f(app)s(eared)g(in)f
(STOC'86.)257 2516 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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257 2516 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.BCST92) cvn H.B /DEST pdfmark
end
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(Barrington,)i(K.)e(J.)h(Compton,)g(H.)f(Straubing,)i(and)e(D.)g
(Th\351rien.)40 b(Regular)447 2766 y(languages)31 b(in)g(nc)1055
2733 y Fw(1)1094 2766 y Fz(.)41 b Fd(J.)32 b(Comput.)g(Syst.)f(Sci.)p
Fz(,)f(44\(3\):478\025499,)i(1992.)257 2792 y
SDict begin H.S end
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a 257 2792 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BarringtonIS90) cvn H.B
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a Fz([9])49 b(D.)28 b(A.)f(M.)h(Barrington,)i(N.)d(Immerman,)j(and)e
(H.)g(Straubing.)38 b(On)28 b(uniformit)m(y)h(within)447
3037 y(nc.)40 b Fd(J.)33 b(Comput.)e(Syst.)h(Sci.)p Fz(,)e
(41\(3\):274\025306,)i(1990.)257 3064 y
SDict begin H.S end
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3064 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BarringtonS95) cvn H.B /DEST
pdfmark end
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b(D.)23 b(A.)f(M.)h(Barrington)h(and)g(H.)f(Straubing.)29
b(Sup)s(erlinear)c(lo)m(w)m(er)f(b)s(ounds)f(for)g(b)s(ounded-)447
3308 y(width)31 b(branc)m(hing)h(programs.)42 b Fd(J.)32
b(Comput.)g(Syst.)f(Sci.)p Fz(,)f(50\(3\):374\025381,)i(1995.)257
3335 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BarringtonST90) cvn H.B
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3335 a 132 x Fz([11])50 b(D.)33 b(A.)f(M.)h(Barrington,)i(H.)d
(Straubing,)k(and)d(D.)g(Th\351rien.)49 b(Non-uniform)34
b(automata)447 3580 y(o)m(v)m(er)d(groups.)41 b Fd(Information)31
b(and)h(Computation)p Fz(,)e(89\(2\):109\025132,)i(1990.)257
3606 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BarringtonT88) cvn H.B /DEST
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3606 a 132 x Fz([12])50 b(D.)34 b(A.)f(M.)h(Barrington)h(and)f(D.)g
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y Fz(.)40 b Fd(Journal)33 b(of)f(the)h(A)n(CM)p Fz(,)c
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SDict begin H.S end
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a 257 3878 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BeamePS05) cvn H.B /DEST
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b(\(ICALP'05\))p Fz(,)447 4348 y(pages)30 b(1176\0251188,)i(2005.)257
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SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BergadanoV96) cvn H.B /DEST
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4370 a 137 x Fz([14])50 b(F.)29 b(Bergadano)i(and)g(S.)e(V)-8
b(arricc)m(hio.)42 b(Learning)31 b(b)s(eha)m(viors)f(of)g(automata)h
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SDict begin H.S end
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a 257 4646 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BDLMT97) cvn H.B /DEST pdfmark
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5004 y(Complexity)p Fz(,)k(pages)h(193\025203,)g(1997.)257
5026 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.BilardiP90) cvn H.B /DEST
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SDict begin [ /View [/XYZ H.V] /Dest (cite.CKSTT06) cvn H.B /DEST pdfmark
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b(,)37 b(A.)c(Krebs,)h(M.)f(Szegedy)-8 b(,)35 b(P)-8
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SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.CohenPP93) cvn H.B /DEST
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1653 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.ComptonS01) cvn H.B /DEST
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1653 a 134 x Fz([21])50 b(K.)21 b(J.)g(Compton)h(and)g(H.)e(Straubing.)
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2012 y(pages)30 b(235\025246.)i(2001.)257 2036 y
SDict begin H.S end
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2036 a 257 2036 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.DKMW) cvn H.B /DEST pdfmark
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x Fz([22])50 b(C.)21 b(Damm,)i(M.)e(Krause,)i(C.)e(Meinel,)i(and)e(S.)g
(W)-8 b(aac)m(k.)26 b(On)21 b(relations)h(b)s(et)m(w)m(een)g(coun)m
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Fd(J.)f(Comput.)g(Syst.)e(Sci.)p Fz(,)h(69\(2\):259\025280,)i(2004.)257
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SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.Eilenberg) cvn H.B /DEST
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2316 a 134 x Fz([23])50 b(S.)24 b(Eilen)m(b)s(erg.)31
b Fd(A)n(utomata,)c(L)-5 b(anguages)28 b(and)e(Machines)p
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y(1976.)257 2569 y
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.EsikW05) cvn H.B /DEST pdfmark
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2838 y(Comput.)32 b(Sci.)p Fz(,)d(340\(1\):291\025321,)k(2005.)257
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SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.FurstSS84) cvn H.B /DEST
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3226 y(v)m(ersion)f(app)s(eared)g(in)f(F)m(OCS'81.)257
3250 y
SDict begin H.S end
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SDict begin 13.6 H.A end
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y(o)m(v)m(er)c(monoids.)41 b Fd(Information)31 b(and)h(Computation)p
Fz(,)e(2006.)41 b(T)-8 b(o)31 b(app)s(ear.)257 3525 y
SDict begin H.S end

257 3525 a 257 3525 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.GavaldaT03) cvn H.B /DEST
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3889 y(\(ST)-7 b(A)n(CS'03\))p Fz(,)28 b(2003.)257 3918
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SDict begin H.S end
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SDict begin 13.6 H.A end
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a 134 x Fz([28])50 b(V.)41 b(Grolm)m(usz.)74 b(Separating)43
b(the)f(comm)m(unication)i(complexities)e(of)f(MOD)h
Fc(m)f Fz(and)447 4165 y(MOD)30 b Fc(p)g Fz(circuits.)41
b(In)30 b Fd(Pr)-5 b(o)g(c.)33 b(33r)-5 b(d)33 b(IEEE)g(F)n(OCS)p
Fz(,)c(pages)i(278\025287,)g(1992.)257 4188 y
SDict begin H.S end
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a 257 4188 a
SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.Grolmusz94b) cvn H.B /DEST
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b(V.)30 b(Grolm)m(usz.)41 b(The)31 b(BNS)f(lo)m(w)m(er)i(b)s(ound)f
(for)f(m)m(ulti-part)m(y)j(proto)s(cols)d(in)h(nearly)f(opti-)447
4440 y(mal.)41 b Fd(Information)30 b(and)j(Computation)p
Fz(,)c(112\(1\):51\02554,)k(1994.)257 4468 y
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SDict begin 13.6 H.A end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.HansenMV03) cvn H.B /DEST
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b(.)34 b(B.)f(Miltersen,)h(and)g(V.)f(Vina)m(y)-8 b(.)49
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SDict begin H.S end
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SDict begin 13.6 H.A end
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SDict begin [ /View [/XYZ H.V] /Dest (cite.HertrampfEtAl93) cvn H.B
/DEST pdfmark end
 257 473 a 100 x Fz([33])50
b(U.)40 b(Hertrampf,)k(C.)d(Lautemann,)46 b(T.)41 b(Sc)m(h)m(w)m(en)m
(tic)m(k,)47 b(H.)40 b(V)-8 b(ollmer,)45 b(and)c(K.)g(W)-8
b(agner.)447 686 y(On)40 b(the)h(p)s(o)m(w)m(er)g(of)f(p)s(olynomial)h
(time)g(bit-reductions.)72 b(In)39 b Fd(Conf.)h(on)i(Structur)-5
b(e)43 b(in)447 799 y(Complexity)32 b(The)-5 b(ory)p
Fz(,)31 b(1993.)257 819 y
SDict begin H.S end
 257 819 a 257 819 a
SDict begin 13.6 H.A end
 257 819
a 257 819 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.JeavonsCG97) cvn H.B /DEST
pdfmark end
 257 819 a 134 x Fz([34])50 b(P)-8 b(.)42
b(Jea)m(v)m(ons,)47 b(D.)41 b(Cohen,)46 b(and)c(M.)f(Gyssens.)74
b(Closure)42 b(prop)s(erties)g(of)g(constrain)m(ts.)447
1066 y Fd(J.)32 b(A)n(CM)p Fz(,)d(44\(4\):527\025548,)k(1997.)257
1091 y
SDict begin H.S end
 257 1091 a 257 1091 a
SDict begin 13.6 H.A end
 257 1091 a 257 1091 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.JennerMT94) cvn H.B /DEST
pdfmark end
 257
1091 a 130 x Fz([35])50 b(B.)23 b(Jenner,)k(P)-8 b(.)24
b(McKenzie,)i(and)e(D.)g(Th\351rien.)31 b(Logspace)24
b(and)h(logtime)f(leaf)g(languages.)447 1334 y(In)35
b Fd(Pr)-5 b(o)g(c)g(e)g(e)g(dings)40 b(of)c(the)i(Ninth)e(A)n(nnual)g
(Structur)-5 b(e)39 b(in)d(Complexity)g(The)-5 b(ory)37
b(Confer-)447 1447 y(enc)-5 b(e)p Fz(,)32 b(pages)e(242\025254.)i(IEEE)
f(Computer)h(So)s(ciet)m(y)f(Press,)f(1994.)257 1467
y
SDict begin H.S end
 257 1467 a 257 1467 a
SDict begin 13.6 H.A end
 257 1467 a 257 1467 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Kamp68) cvn H.B /DEST pdfmark
end
 257 1467
a 135 x Fz([36])50 b(J.)36 b(A.)g(W.)g(Kamp.)58 b Fd(T)-7
b(ense)38 b(L)-5 b(o)g(gic)39 b(and)e(the)h(The)-5 b(ory)38
b(of)f(Line)-5 b(ar)38 b(Or)-5 b(der)p Fz(.)58 b(PhD)37
b(thesis,)447 1715 y(Univ)m(ersit)m(y)31 b(of)f(California,)h(Berk)m
(eley)-8 b(,)32 b(1968.)257 1735 y
SDict begin H.S end
 257 1735 a 257 1735
a
SDict begin 13.6 H.A end
 257 1735 a 257 1735 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.KarchmerNSW94) cvn H.B /DEST
pdfmark end
 257 1735 a 134 x Fz([37])50 b(M.)30
b(Karc)m(hmer,)i(I.)e(Newman,)h(M.)f(E.)h(Saks,)f(and)h(A.)f
(Wigderson.)41 b(Non-deterministic)447 1982 y(comm)m(unication)63
b(complexit)m(y)e(with)g(few)f(witnesses.)130 b Fd(J.)60
b(Comput.)f(Syst.)g(Sci.)p Fz(,)447 2095 y(49\(2\):247\025257,)32
b(1994.)257 2120 y
SDict begin H.S end
 257 2120 a 257 2120 a
SDict begin 13.6 H.A end
 257 2120 a 257
2120 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.KouckyPT05) cvn H.B /DEST
pdfmark end
 257 2120 a 130 x Fz([38])50 b(M.)41 b(K)m(ouc)m(k\375,)k(P)-8
b(.)42 b(Pudl\341k,)j(and)d(D.)f(Th\351rien.)75 b(Bounded-depth)43
b(circuits:)63 b(separat-)447 2363 y(ing)41 b(wires)h(from)f(gates.)74
b(In)41 b Fd(Pr)-5 b(o)g(c.)43 b(37th)g(A)n(CM)e(Symp.)g(on)i(The)-5
b(ory)42 b(of)h(Computing)447 2476 y(\(STOC'05\))p Fz(,)29
b(pages)h(257\025265,)i(2005.)257 2501 y
SDict begin H.S end
 257 2501 a 257
2501 a
SDict begin 13.6 H.A end
 257 2501 a 257 2501 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.KrebsLR05) cvn H.B /DEST
pdfmark end
 257 2501 a 139 x Fz([39])50
b(A.)36 b(Krebs,)i(K.-J.)f(Lange,)i(and)e(S.)g(Rei\033ersc)m(heid.)59
b(Characterizing)38 b(tc)2967 2607 y(0)3053 2640 y(in)f(terms)f(of)447
2753 y(in\034nite)21 b(groups.)k(In)20 b Fd(Pr)-5 b(o)g(c.)25
b(22nd)e(Symp.)f(on)h(The)-5 b(or)g(etic)g(al)26 b(Asp)-5
b(e)g(cts)25 b(of)e(CS)f(\(ST)-7 b(A)n(CS'05\))p Fz(,)447
2866 y(pages)30 b(496\025507,)i(2005.)257 2886 y
SDict begin H.S end
 257
2886 a 257 2886 a
SDict begin 13.6 H.A end
 257 2886 a 257 2886 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.KN97) cvn H.B /DEST pdfmark
end
 257 2886 a 135
x Fz([40])50 b(E.)37 b(Kushilevitz)h(and)f(N.)g(Nisan.)60
b Fd(Communic)-5 b(ation)37 b(Complexity)p Fz(.)60 b(Cam)m(bridge)39
b(Uni-)447 3134 y(v)m(ersit)m(y)31 b(Press,)f(1997.)257
3154 y
SDict begin H.S end
 257 3154 a 257 3154 a
SDict begin 13.6 H.A end
 257 3154 a 257 3154 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.McKenziePT91) cvn H.B /DEST
pdfmark end
 257
3154 a 135 x Fz([41])50 b(P)-8 b(.)40 b(McKenzie,)j(P)-8
b(.)41 b(P\351ladeau,)i(and)d(D.)g(Th\351rien.)69 b(NC)2415
3256 y Fw(1)2454 3289 y Fz(:)59 b(The)40 b(automata)h(theoretic)447
3402 y(viewp)s(oin)m(t.)g Fd(Computational)32 b(Complexity)p
Fz(,)e(1:330\025359,)i(1991.)257 3421 y
SDict begin H.S end
 257 3421 a 257
3421 a
SDict begin 13.6 H.A end
 257 3421 a 257 3421 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.McnaughtonP) cvn H.B /DEST
pdfmark end
 257 3421 a 135 x Fz([42])50
b(R.)36 b(McNaugh)m(ton)i(and)g(S.)e(P)m(ap)s(ert.)61
b Fd(Counter-F)-7 b(r)i(e)g(e)41 b(A)n(utomata)p Fz(.)59
b(MIT)37 b(Press,)h(Cam-)447 3669 y(bridge,)31 b(Mass.,)f(1971.)257
3689 y
SDict begin H.S end
 257 3689 a 257 3689 a
SDict begin 13.6 H.A end
 257 3689 a 257 3689 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Nisan94) cvn H.B /DEST pdfmark
end
 257
3689 a 135 x Fz([43])50 b(N.)23 b(Nisan.)30 b(The)24
b(comm)m(unication)j(complexit)m(y)e(of)e(treshold)i(gates.)30
b(In)23 b Fd(Combinatorics,)447 3937 y(Paul)33 b(Er)-5
b(d\366s)33 b(is)f(Eighty,)g(V)-7 b(ol.)32 b(1)p Fz(,)e(pages)h
(301\025315,)g(1993.)257 3957 y
SDict begin H.S end
 257 3957 a 257 3957 a
SDict begin 13.6 H.A end

257 3957 a 257 3957 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.PeladeauT88) cvn H.B /DEST
pdfmark end
 257 3957 a 135 x Fz([44])50 b(P)-8
b(.)29 b(P)m(\351ladeau)g(and)g(D.)f(Th\351rien.)37 b(Sur)28
b(les)g(langages)h(reconn)m(us)g(par)f(des)g(group)s(es)g(nilp)s(o-)447
4205 y(ten)m(ts.)61 b Fd(C.R.)37 b(A)-5 b(c)g(ad.)40
b(des)f(Sci.)f(Paris)h(S\351r.)f(I)g(Math.)p Fz(,)h(306\(2\):93\02595,)
i(1988.)61 b(English)447 4317 y(translation)31 b(b)m(y)g(A.)f(Russell)g
(and)g(S.)h(Russell)e(app)s(ears)i(as)f(TR01-040)h(of)f(ECCC.)257
4337 y
SDict begin H.S end
 257 4337 a 257 4337 a
SDict begin 13.6 H.A end
 257 4337 a 257 4337 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Pin) cvn H.B /DEST pdfmark
end
 257
4337 a 135 x Fz([45])50 b(J.-E.)33 b(Pin.)46 b Fd(V)-7
b(arieties)34 b(of)g(formal)f(languages)p Fz(.)47 b(North)33
b(Oxford)f(A)m(cademic)h(Publishers)447 4585 y(Ltd,)e(London,)h(1986.)
257 4605 y
SDict begin H.S end
 257 4605 a 257 4605 a
SDict begin 13.6 H.A end
 257 4605 a 257 4605
a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Pin97) cvn H.B /DEST pdfmark
end
 257 4605 a 135 x Fz([46])50 b(J.-E.)30 b(Pin.)39 b(Syn)m(tactic)30
b(semigroups.)39 b(In)29 b(G.)g(R.)g(et)g(A.)g(Salomaa,)h(editor,)g
Fd(Handb)-5 b(o)g(ok)33 b(of)447 4853 y(language)h(the)-5
b(ory)p Fz(,)31 b(v)m(olume)g(1,)g(c)m(hapter)h(10,)e(pages)h
(679\025746.)h(Springer)f(V)-8 b(erlag,)32 b(1997.)257
4873 y
SDict begin H.S end
 257 4873 a 257 4873 a
SDict begin 13.6 H.A end
 257 4873 a 257 4873 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.PinW96) cvn H.B /DEST pdfmark
end
 257
4873 a 135 x Fz([47])50 b(J.)28 b(E.)h(Pin)f(and)h(P)-8
b(.)29 b(W)-8 b(eil.)37 b(Pro\034nite)30 b(semigroups,)f(Mal'cev)f(pro)
s(ducts,)h(and)f(iden)m(tities.)447 5120 y Fd(Journal)33
b(of)f(A)n(lgebr)-5 b(a)p Fz(,)32 b(182:604\025626,)g(1996.)257
5140 y
SDict begin H.S end
 257 5140 a 257 5140 a
SDict begin 13.6 H.A end
 257 5140 a 257 5140 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.PinW97) cvn H.B /DEST pdfmark
end
 257
5140 a 135 x Fz([48])50 b(J.)29 b(E.)h(Pin)g(and)f(P)-8
b(.)31 b(W)-8 b(eil.)39 b(P)m(olynomial)31 b(closure)f(and)f(unam)m
(biguous)j(pro)s(duct.)39 b Fd(The)-5 b(ory)447 5388
y(Comput.)32 b(Systems)p Fz(,)d(30:383\025422,)j(1997.)p
eop end
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SDict begin H.S end
 257 266
a 257 266 a
SDict begin H.R end
 257 266 a 257 266 a
SDict begin [ /View [/XYZ H.V] /Dest (page.29) cvn H.B /DEST pdfmark
end
 257 266 a 257 473 a
SDict begin H.S end
 257
473 a 257 473 a
SDict begin 13.6 H.A end
 257 473 a 257 473 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Pudlak03) cvn H.B /DEST
pdfmark end
 257 473 a 100 x Fz([49])50
b(P)-8 b(.)32 b(Pudl\341k.)45 b(An)32 b(application)h(of)f(Hindman's)g
(theorem)h(to)f(a)f(problem)i(on)f(comm)m(uni-)447 686
y(cation)g(complexit)m(y)-8 b(.)45 b(T)-8 b(o)32 b(app)s(ear)g(in)g
Fb(Com)m(binatorics,)i(Probabilit)m(y)f(and)f(Computing)p
Fz(,)447 799 y(2003.)257 805 y
SDict begin H.S end
 257 805 a 257 805 a
SDict begin 13.6 H.A end
 257
805 a 257 805 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.RaymondTT98) cvn H.B /DEST
pdfmark end
 257 805 a 157 x Fz([50])50 b(J.-F.)37
b(Ra)m(ymond,)h(P)-8 b(.)37 b(T)-8 b(esson,)38 b(and)f(D.)f
(Th\351rien.)59 b(An)36 b(algebraic)h(approac)m(h)h(to)e(com-)447
1075 y(m)m(unication)52 b(complexit)m(y)-8 b(.)99 b Fd(L)-5
b(e)g(ctur)g(e)53 b(Notes)d(in)g(Computer)g(Scienc)-5
b(e)51 b(\(ICALP'98\))p Fz(,)447 1187 y(1443:29\02540,)32
b(1998.)257 1211 y
SDict begin H.S end
 257 1211 a 257 1211 a
SDict begin 13.6 H.A end
 257 1211 a 257
1211 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.RazM97) cvn H.B /DEST pdfmark
end
 257 1211 a 139 x Fz([51])50 b(R.)26 b(Raz)h(and)g(P)-8
b(.)27 b(McKenzie.)36 b(Separation)29 b(of)d(the)h(monotone)h
Fc(N)10 b(C)33 b Fz(hierarc)m(h)m(y)-8 b(.)38 b(In)26
b Fd(Pr)-5 b(o)g(c.)447 1463 y(38)539 1430 y Ft(th)609
1463 y Fd(th)33 b(IEEE)f(F)n(OCS)p Fz(,)d(1997.)257 1487
y
SDict begin H.S end
 257 1487 a 257 1487 a
SDict begin 13.6 H.A end
 257 1487 a 257 1487 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Schutzenberger65) cvn H.B
/DEST pdfmark end
 257 1487
a 139 x Fz([52])50 b(M.)34 b(P)-8 b(.)36 b(Sc)m(h)m(\374tzen)m(b)s
(erger.)56 b(On)35 b(\034nite)h(monoids)f(ha)m(ving)h(only)f(trivial)g
(subgroups.)53 b Fd(In-)447 1739 y(formation)31 b(and)h(Contr)-5
b(ol)p Fz(,)30 b(8\(2\):190\025194,)j(1965.)257 1768
y
SDict begin H.S end
 257 1768 a 257 1768 a
SDict begin 13.6 H.A end
 257 1768 a 257 1768 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Simon75) cvn H.B /DEST pdfmark
end
 257 1768
a 134 x Fz([53])50 b(I.)35 b(Simon.)56 b(Piecewise)37
b(testable)f(ev)m(en)m(ts.)57 b(In)35 b Fd(Pr)-5 b(o)g(c.)38
b(2nd)f(GI)g(Conf.)p Fz(,)e(pages)h(214\025222,)447 2015
y(1975.)257 2021 y
SDict begin H.S end
 257 2021 a 257 2021 a
SDict begin 13.6 H.A end
 257 2021 a 257
2021 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Smolensky87) cvn H.B /DEST
pdfmark end
 257 2021 a 157 x Fz([54])50 b(R.)33 b(Smolensky)-8
b(.)50 b(Algebraic)34 b(metho)s(ds)g(in)f(the)h(theory)g(of)f(lo)m(w)m
(er)i(b)s(ounds)f(for)f(b)s(o)s(olean)447 2291 y(circuit)e(complexit)m
(y)-8 b(.)42 b(In)30 b Fd(Pr)-5 b(o)g(c.)34 b(19)1658
2258 y Ft(th)1760 2291 y Fd(A)n(CM)e(STOC)p Fz(,)d(pages)h(77\02582,)i
(1986.)257 2315 y
SDict begin H.S end
 257 2315 a 257 2315 a
SDict begin 13.6 H.A end
 257 2315 a 257
2315 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Straubing94) cvn H.B /DEST
pdfmark end
 257 2315 a 139 x Fz([55])50 b(H.)22 b(Straubing.)30
b Fd(Finite)25 b(A)n(utomata,)h(F)-7 b(ormal)26 b(L)-5
b(o)g(gic)26 b(and)f(Cir)-5 b(cuit)26 b(Complexity)p
Fz(.)i(Boston:)447 2567 y(Birkhauser,)j(1994.)257 2591
y
SDict begin H.S end
 257 2591 a 257 2591 a
SDict begin 13.6 H.A end
 257 2591 a 257 2591 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Straubing00) cvn H.B /DEST
pdfmark end
 257 2591
a 139 x Fz([56])50 b(H.)28 b(Straubing.)40 b(When)29
b(can)g(one)g(monoid)h(sim)m(ulate)g(another?)49 b(In)29
b Fd(A)n(lgorithmic)i(Pr)-5 b(ob-)447 2843 y(lems)32
b(in)g(Gr)-5 b(oups)33 b(and)f(Semigr)-5 b(oups)p Fz(,)31
b(pages)g(267\025288.)h(Birkh\344user,)e(2000.)257 2867
y
SDict begin H.S end
 257 2867 a 257 2867 a
SDict begin 13.6 H.A end
 257 2867 a 257 2867 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Straubing01) cvn H.B /DEST
pdfmark end
 257 2867
a 139 x Fz([57])50 b(H.)39 b(Straubing.)69 b(Languages)41
b(de\034ned)g(b)m(y)f(mo)s(dular)g(quan)m(ti\034ers.)69
b Fd(Information)39 b(and)447 3118 y(Computation)p Fz(,)29
b(166:112\025132,)k(2001.)257 3142 y
SDict begin H.S end
 257 3142 a 257 3142
a
SDict begin 13.6 H.A end
 257 3142 a 257 3142 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Straubing02) cvn H.B /DEST
pdfmark end
 257 3142 a 139 x Fz([58])50 b(H.)29
b(Straubing.)41 b(On)30 b(the)g(logical)h(description)g(of)e(regular)i
(languages.)41 b(In)29 b Fd(Pr)-5 b(o)g(c.)33 b(of)f(the)447
3394 y(5th)g(L)-5 b(atin)32 b(A)n(meric)-5 b(an)33 b(The)-5
b(or)g(etic)g(al)34 b(Informatics)d(Confer)-5 b(enc)g(e)34
b(\(LA)-7 b(TIN)31 b('02\))p Fz(,)f(2002.)257 3423 y
SDict begin H.S end

257 3423 a 257 3423 a
SDict begin 13.6 H.A end
 257 3423 a 257 3423 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.StraubingT01) cvn H.B /DEST
pdfmark end
 257 3423
a 134 x Fz([59])50 b(H.)29 b(Straubing)j(and)e(D.)g(Th\351rien.)41
b(Regular)31 b(languages)g(de\034ned)g(b)m(y)f(generalized)i(\034rst-)
447 3670 y(order)i(form)m(ulas)h(with)g(a)f(b)s(ounded)g(n)m(um)m(b)s
(er)i(of)d(b)s(ound)i(v)-5 b(ariables.)51 b(In)34 b Fd(Pr)-5
b(o)g(c.)37 b(of)e(18th)447 3783 y(Symp.)c(on)g(The)-5
b(or)g(etic)g(al)34 b(Asp)-5 b(e)g(cts)34 b(of)d(Comp.)g(Sci.)g(c)-5
b(onfer)g(enc)g(e)p Fz(,)33 b(pages)d(551\025562,)h(2001.)257
3807 y
SDict begin H.S end
 257 3807 a 257 3807 a
SDict begin 13.6 H.A end
 257 3807 a 257 3807 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.StraubingTT95) cvn H.B /DEST
pdfmark end
 257
3807 a 139 x Fz([60])50 b(H.)41 b(Straubing,)k(D.)c(Th\351rien,)k(and)d
(W.)f(Thomas.)73 b(Regular)42 b(languages)g(de\034ned)g(b)m(y)447
4059 y(generalized)32 b(quan)m(ti\034ers.)41 b Fd(Information)31
b(and)h(Computation)p Fz(,)e(\(118\):289\025301,)j(1995.)257
4088 y
SDict begin H.S end
 257 4088 a 257 4088 a
SDict begin 13.6 H.A end
 257 4088 a 257 4088 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Szegedy93) cvn H.B /DEST
pdfmark end
 257
4088 a 134 x Fz([61])50 b(M.)44 b(Szegedy)-8 b(.)83 b(F)-8
b(unctions)46 b(with)f(b)s(ounded)g(symmetric)g(comm)m(unication)i
(complex-)447 4335 y(it)m(y)-8 b(,)39 b(programs)e(o)m(v)m(er)h(comm)m
(utativ)m(e)h(monoids,)g(and)e(A)m(CC.)59 b Fd(J.)38
b(Comput.)g(Syst.)f(Sci.)p Fz(,)447 4448 y(47\(3\):405\025423,)32
b(1993.)257 4477 y
SDict begin H.S end
 257 4477 a 257 4477 a
SDict begin 13.6 H.A end
 257 4477 a 257
4477 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.Tesson03) cvn H.B /DEST
pdfmark end
 257 4477 a 134 x Fz([62])50 b(P)-8 b(.)39 b(T)-8
b(esson.)67 b Fd(Computational)39 b(Complexity)h(Questions)g(R)-5
b(elate)g(d)42 b(to)e(Finite)g(Monoids)447 4724 y(and)32
b(Semigr)-5 b(oups)p Fz(.)41 b(PhD)31 b(thesis,)f(McGill)h(Univ)m
(ersit)m(y)-8 b(,)31 b(2003.)257 4748 y
SDict begin H.S end
 257 4748 a 257
4748 a
SDict begin 13.6 H.A end
 257 4748 a 257 4748 a
SDict begin [ /View [/XYZ H.V] /Dest (cite.TessonT02b) cvn H.B /DEST
pdfmark end
 257 4748 a 138 x Fz([63])50
b(P)-8 b(.)50 b(T)-8 b(esson)50 b(and)g(D.)f(Th\351rien.)98
b(Diamonds)50 b(are)g(forev)m(er:)79 b(the)49 b(v)-5
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