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1879 V 100 w(an)m(y)30 b Fm(k)p 1715 1879 V 763 w(d)c Fw(=)f Fm(O)s Fw(\(log)2160 1809 y Fo(2)2214 1845 y Fm(n)p Fw(\))p 2839 1879 V 586 w Fm(m)g Fw(=)g(\012\()p Fm(k)s Fw(\))p 3647 1879 V 3664 1879 V 235 1883 3431 4 v 233 1996 4 113 v 250 1996 V 301 1962 a([ISW00)q(])p 733 1996 V 166 w(an)m(y)30 b Fm(k)p 1715 1996 V 763 w(d)c Fw(=)f Fm(O)s Fw(\(log)17 b Fm(n)p Fw(\))p 2839 1996 V 625 w Fm(m)25 b Fw(=)g Fm(k)3141 1929 y Fo(1)p Fi(\000)p Fj(\016)p 3647 1996 V 3664 1996 V 235 1999 3431 4 v 233 2112 4 113 v 250 2112 V 301 2078 a Fw([RSW00)q(])p 733 2112 V 132 w(an)m(y)30 b Fm(k)p 1715 2112 V 763 w(d)c Fw(=)f Fm(O)s Fw(\(log)17 b Fm(n)j Fl(\001)g Fw(\(log)d(log)g Fm(n)p Fw(\))2686 2045 y Fo(2)2725 2078 y Fw(\))p 2839 2112 V 130 w Fm(m)25 b Fw(=)g(\012\()p Fm(k)s Fw(\))p 3647 2112 V 3664 2112 V 235 2115 3431 4 v 233 2228 4 113 v 250 2228 V 301 2194 a([RSW00)q(])p 733 2228 V 132 w(an)m(y)30 b Fm(k)p 1715 2228 V 763 w(d)c Fw(=)f Fm(O)s Fw(\(log)17 b Fm(n)p Fw(\))p 2839 2228 V 625 w Fm(m)25 b 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b(Raz,)i(O.)f(Reingold,)f(and)g(S.)g(V)-8 b(adhan.)52 b(Error)34 b(reduction)f(for)h(extractors.)54 b(In)34 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)503 1219 y(of)32 b(the)h(40th)i(A)n(nnual)d(IEEE)g(Symp)-5 b(osium)34 b(on)f(F)-7 b(oundations)35 b(of)e(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(1999.)0 1406 y([RR)-10 b(V99b])120 b(R.)28 b(Raz,)i(O.)f(Reingold,)f(and)g(S.)h(V)-8 b(adhan.)38 b(Extracting)29 b(all)f(the)h(randomness)e(and)h(reducing)g(the)503 1519 y(error)j(in)f(trevisan's)h(extractors.)46 b(In)31 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)36 b(of)e(the)g(31st)h(A)n(CM)d (Symp)-5 b(osium)36 b(on)e(The)-5 b(ory)503 1632 y(of)32 b(Computing)p Fw(,)g(pages)f(149{158,)j(1999.)0 1820 y([RSW00])152 b(O.)43 b(Reingold,)i(R.)f(Shaltiel,)g(and)f(A.)h (Wigderson.)78 b(Extracting)44 b(randomness)e(via)h(rep)s(eated)503 1933 y(condensing.)57 b(In)36 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)41 b(of)d(the)h(41st)g(A)n(nnual)g(IEEE)e(Symp)-5 b(osium)40 b(on)f(F)-7 b(oundations)41 b(of)503 2046 y(Computer)34 b(Scienc)-5 b(e)p Fw(,)30 b(2000.)0 2233 y([R)-8 b(TS97])187 b(Jaikumar)34 b(Radhakrishnan)g(and)i(Amnon)f(T)-8 b(a-Shma.)58 b(Tigh)m(t)36 b(b)s(ounds)e(for)i(depth-t)m(w)m(o)h(sup)s(er-)503 2346 y(concen)m(trators.)32 b(In)24 b Fn(38th)29 b(A)n(nnual)e(Symp)-5 b(osium)29 b(on)e(F)-7 b(oundations)30 b(of)d(Computer)i(Scienc)-5 b(e)p Fw(,)25 b(pages)503 2459 y(585{594,)33 b(Miami)d(Beac)m(h,)i (Florida,)d(20{22)k(Octob)s(er)d(1997.)i(IEEE.)0 2647 y([R)-8 b(TS00])187 b(J.)30 b(Radhakrishnan)e(and)i(A.)h(T)-8 b(a-Shma.)41 b(Bounds)30 b(for)g(disp)s(ersers,)f(extractors,)j(and)e (depth-t)m(w)m(o)503 2760 y(sup)s(erconcen)m(trators.)75 b Fn(SIAM)43 b(Journal)h(on)g(Discr)-5 b(ete)43 b(Mathematics)p Fw(,)k(13\(1\):2{24,)i(F)-8 b(ebruary)503 2873 y(2000.)0 3060 y([R)e(VW00])145 b(Omer)31 b(Reingold,)g(Salil)e(V)-8 b(adhan,)33 b(and)e(Avi)g(Wigderson.)44 b(En)m(trop)m(y)32 b(w)m(a)m(v)m(es,)i(the)e(zig-zag)h(graph)503 3173 y(pro)s(duct,)24 b(and)g(new)g(constan)m(t-degree)j(expanders)c(and)h(extractors.)32 b(In)24 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)29 b(of)e(the)h(41st)503 3286 y(A)n(nnual)k(IEEE)g(Symp)-5 b(osium)34 b(on)f(F)-7 b(oundations)35 b(of)e(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(2000.)0 3474 y([RZ98])240 b(A.)40 b(Russell)f(and)h(D.)h(Zuc)m(k)m (erman.)70 b(P)m(erfect-information)40 b(leader)g(election)h(in)e(log) 3478 3437 y Fi(\003)3533 3474 y Fm(n)26 b Fw(+)h Fm(O)s Fw(\(1\))503 3587 y(rounds.)34 b Fn(Journal)d(of)f(Computer)h(and)g (System)g(Scienc)-5 b(es)p Fw(,)28 b(1998.)38 b(T)-8 b(o)28 b(app)s(ear.)f(Preliminary)d(v)m(er-)503 3699 y(sion)i(in)f Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)32 b(of)e(the)g(39th)h (A)n(nnual)e(IEEE)g(Symp)-5 b(osium)32 b(on)e(F)-7 b(oundations)32 b(of)e(Computer)503 3812 y(Scienc)-5 b(e)p Fw(,)30 b(pages)h(576{583.)0 4000 y([Sip88])235 b(M.)36 b(Sipser.)54 b(Expanders,)36 b(randomness,)f(or)h(time)f(v)m(ersus)g(space.)57 b Fn(Journal)39 b(of)e(Computer)i(and)503 4113 y(System)33 b(Scienc)-5 b(es)p Fw(,)30 b(36,)i(1988.)0 4301 y([SSZ98])205 b(M.)41 b(Saks,)i(A.)e(Sriniv)-5 b(asan,)41 b(and)f(S.)g(Zhou.)71 b(Explicit)38 b(OR-disp)s(ersers)g(with)i(p)s(olylogarithmic)503 4413 y(degree.)h Fn(Journal)34 b(of)e(the)h(A)n(CM)p Fw(,)d(45\(1\):123{154,)36 b(Jan)m(uary)30 b(1998.)0 4601 y([STV99])178 b(Madh)m(u)34 b(Sudan,)h(Luca)g(T)-8 b(revisan,)36 b(and)f(Salil)d(V)-8 b(adhan.)55 b(Pseudorandom)34 b(generators)i(without)503 4714 y(the)25 b(xor)g(lemma.)32 b(In)24 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)30 b(of)e(the)g (Thirty-First)h(A)n(nnual)f(A)n(CM)e(Symp)-5 b(osium)30 b(on)e(The)-5 b(ory)503 4827 y(of)32 b(Computing)p Fw(,)g(1999.)0 5015 y([SU01])244 b(R.)30 b(Shaltiel)f(and)h(C.)g(Umans.)42 b(Simple)28 b(extractors)k(for)e(all)g(min-en)m(tropies)f(and)h(a)h (new)f(pseudo-)503 5127 y(random)i(generator.)52 b(In)33 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)37 b(of)f(the)g(42nd)h(A)n(nnual)f (IEEE)e(Symp)-5 b(osium)38 b(on)e(F)-7 b(ounda-)503 5240 y(tions)33 b(of)g(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(2001.)p eop %%Page: 28 28 28 27 bop 0 91 a Fw([Sud97])210 b(M.)26 b(Sudan.)33 b(Deco)s(ding)26 b(of)g(Reed)h(Solomon)e(co)s(des)i(b)s(ey)m(ond)e(the)i (error-correction)f(b)s(ound.)32 b Fn(Jour-)503 204 y(nal)h(of)g (Complexity)p Fw(,)f(13,)g(1997.)0 389 y([SV86])244 b(M.)26 b(San)m(tha)h(and)f(U.)g(V.)h(V)-8 b(azirani.)33 b(Generating)27 b(quasi-random)e(sequences)h(from)g(semi-random)503 501 y(sources.)40 b Fn(Journal)34 b(of)f(Computer)h(and)f(System)h(Scienc) -5 b(es)p Fw(,)30 b(33:75{87,)k(1986.)0 686 y([SZ99])256 b(A.)31 b(Sriniv)-5 b(asan)27 b(and)k(D.)g(Zuc)m(k)m(erman.)41 b(Computing)29 b(with)h(v)m(ery)h(w)m(eak)g(random)f(sources.)42 b Fn(SIAM)503 799 y(Journal)33 b(on)g(Computing)p Fw(,)f (28\(4\):1433{1459,)37 b(August)30 b(1999.)0 983 y([T)-8 b(re99])229 b(L.)22 b(T)-8 b(revisan.)26 b(Construction)21 b(of)h(extractors)i(using)d(pseudorandom)f(generators.)28 b(In)22 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)503 1096 y(of)32 b(the)h(31st)h(A)n(CM)e(Symp)-5 b(osium)34 b(on)f(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(1999.)0 1280 y([TS96])246 b(A.)28 b(T)-8 b(a-Shma.)37 b(On)27 b(extracting)i(randomness)e(from)h (w)m(eak)h(random)f(sources.)37 b(In)27 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g (dings)33 b(of)503 1393 y(the)g(28th)h(A)n(nnual)e(A)n(CM)f(Symp)-5 b(osium)35 b(on)e(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(pages)f(276{285,)j(1996.)0 1577 y([TS98])246 b(A.)41 b(T)-8 b(a-Shma.)73 b(Almost)41 b(optimal)g(disp)s(ersers.)70 b(In)41 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)44 b(of)f(the)g(30th)i(A)n (nnual)d(A)n(CM)503 1690 y(Symp)-5 b(osium)33 b(on)f(The)-5 b(ory)33 b(of)f(Computing)h(\(STOC-98\))p Fw(,)d(pages)g(196{202,)j (New)c(Y)-8 b(ork,)30 b(Ma)m(y)h(23{)503 1803 y(26)g(1998.)h(A)m(CM)f (Press.)0 1988 y([TSUZ01])122 b(A.)43 b(T)-8 b(a-Shma,)45 b(C.)e(Umans,)j(and)c(D.)h(Zuc)m(k)m(erman.)77 b(Loss-less)42 b(condensers,)k(un)m(balanced)41 b(ex-)503 2100 y(panders,)48 b(and)d(extractors.)87 b(In)45 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)48 b(of)f(the)g(33r)-5 b(d)48 b(A)n(nnual)f(A)n(CM)e(Symp)-5 b(osium)48 b(on)503 2213 y(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)e(2001.)0 2398 y([TSZ01])190 b(A.)33 b(T)-8 b(a-Shma)33 b(and)f(D.)i(Zuc)m(k)m(erman.)48 b(Extractor)34 b(co)s(des.)48 b(In)32 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)37 b(of)f(the)f(33r)-5 b(d)37 b(A)n(nnual)503 2511 y(A)n(CM)31 b(Symp)-5 b(osium)34 b(on)g(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)e(2001.)0 2695 y([TSZS01])139 b(A.)40 b(T)-8 b(a-Shma,)42 b(D.)e(Zuc)m(k)m (erman,)i(and)e(S.)f(Safra.)68 b(Extractors)41 b(from)e(Reed-Muller)f (co)s(des.)69 b(In)503 2808 y Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)26 b(of)e(the)g(42th)i(A)n(nnual)e(IEEE)f(Symp)-5 b(osium)26 b(on)f(F)-7 b(oundations)26 b(of)f(Computer)g(Scienc)-5 b(e)p Fw(,)503 2921 y(2001.)0 3105 y([TV00])229 b(Luca)24 b(T)-8 b(revisan)23 b(and)h(Salil)e(V)-8 b(adhan.)30 b(Extracting)25 b(randomness)e(from)h(samplable)e(distributions.)503 3218 y(In)44 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)49 b(of)d(the)h(41st)g (A)n(nnual)g(IEEE)e(Symp)-5 b(osium)48 b(on)f(F)-7 b(oundations)49 b(of)e(Computer)503 3331 y(Scienc)-5 b(e)p Fw(,)30 b(2000.)0 3515 y([Uma99])174 b(C.)21 b(Umans.)27 b(Hardness)21 b(of)h(appro)m(ximating)f(\006)2086 3471 y Fj(p)2086 3540 y Fo(2)2147 3515 y Fw(minimization)e(problems.)25 b(In)c Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)26 b(of)g(the)503 3628 y(40th)36 b(A)n(nnual)f(IEEE)g(Symp)-5 b(osium)37 b(on)f(F)-7 b(oundations)38 b(of)d(Computer)i(Scienc)-5 b(e)p Fw(,)34 b(pages)g(465{474,)503 3741 y(1999.)0 3925 y([Uma02])174 b(Chris)38 b(Umans.)73 b(Pseudo-random)40 b(generators)i(for)f(all)f(hardnesses.)71 b(In)40 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)45 b(of)e(the)503 4038 y(Thirty-fourth)34 b(A)n(nnual)e(A)n(CM)g(Symp)-5 b(osium)34 b(on)f(the)g(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(2002.)0 4223 y([V)-8 b(az87a])173 b(Umesh)25 b(V)-8 b(azirani.)32 b(E\016cien)m(t)26 b(considerations)e(in)g(using)h(semi-random)f(sources.)33 b(In)25 b Fn(Pr)-5 b(o)g(c)g(e)g(e)g(dings)503 4335 y(of)32 b(the)h(19th)i(A)n(nnual)d(A)n(CM)f(Symp)-5 b(osium)35 b(on)e(the)g(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(1987.)0 4520 y([V)-8 b(az87b])167 b(Umesh)38 b(V)-8 b(azirani.)64 b(Strong)39 b(comm)m(unication)f(complexit)m(y)g(or)g(generating)h (quasi-random)e(se-)503 4633 y(quences)k(from)g(t)m(w)m(o)h(comm)m (unicating)f(semi-random)f(sources.)73 b Fn(Combinatoric)-5 b(a)p Fw(,)47 b(7:375{392,)503 4746 y(1987.)0 4930 y([vN51])247 b(John)20 b(v)m(on)i(Neumann.)k(V)-8 b(arious)22 b(tec)m(hniques)f (used)g(in)f(connection)i(with)f(random)g(digits.)k Fn(Applie)-5 b(d)503 5043 y(Math)33 b(Series)p Fw(,)d(12:36{38,)k(1951.)0 5227 y([WZ99])214 b(A.)26 b(Wigderson)f(and)g(D.)h(Zuc)m(k)m(erman.)33 b(Expanders)24 b(that)j(b)s(eat)e(the)h(eigen)m(v)-5 b(alue)26 b(b)s(ound:)36 b(Explicit)503 5340 y(construction)29 b(and)h(applications.)39 b Fn(Combinatoric)-5 b(a)p Fw(,)33 b(19\(1\):125{138,)j(1999.)p eop %%Page: 29 29 29 28 bop 0 91 a Fw([Y)-8 b(ao82])213 b(Andrew)22 b(C.)h(Y)-8 b(ao.)31 b(Theory)23 b(and)g(applications)e(of)j(trap)s(do)s(or)e (functions)g(\(extended)i(abstract\).)31 b(In)503 204 y Fn(23r)-5 b(d)34 b(A)n(nnual)d(Symp)-5 b(osium)34 b(on)f(F)-7 b(oundations)34 b(of)f(Computer)g(Scienc)-5 b(e)p Fw(,)30 b(pages)g(80{91,)j(Chicago,)503 317 y(Illinois,)27 b(3{5)k(No)m(v)m(em) m(b)s(er)h(1982.)g(IEEE.)0 505 y([Zuc90])216 b(Da)m(vid)43 b(Zuc)m(k)m(erman.)79 b(General)43 b(w)m(eak)i(random)d(sources.)79 b(In)43 b Fn(31st)j(A)n(nnual)e(Symp)-5 b(osium)46 b(on)503 618 y(F)-7 b(oundations)35 b(of)e(Computer)h(Scienc)-5 b(e)p Fw(,)31 b(v)m(olume)f(I)s(I,)g(pages)h(534{543,)j(St.)d(Louis,)f (Missouri,)f(22{)503 731 y(24)i(Octob)s(er)f(1990.)i(IEEE.)0 918 y([Zuc96a])171 b(D.)27 b(Zuc)m(k)m(erman.)35 b(On)26 b(unappro)m(ximable)e(v)m(ersions)j(of)g(NP-complete)g(problems.)33 b Fn(SIAM)c(Journal)503 1031 y(on)k(Computing)p Fw(,)e(25:1293{1304,)36 b(1996.)0 1219 y([Zuc96b])165 b(D.)35 b(Zuc)m(k)m(erman.)54 b(Sim)m(ulating)32 b(BPP)j(using)f(a)h(general)g(w)m(eak)g(random)f (source.)54 b Fn(A)n(lgorithmic)-5 b(a)p Fw(,)503 1332 y(16\(4/5\):367{391,)36 b(Octob)s(er/No)m(v)m(em)m(b)s(er)c(1996.)0 1519 y([Zuc97])216 b(D.)32 b(Zuc)m(k)m(erman.)45 b(Randomness-optimal) 30 b(oblivious)f(sampling.)43 b Fn(R)-5 b(andom)36 b(Structur)-5 b(es)35 b(and)g(A)n(l-)503 1632 y(gorithms)p Fw(,)d(11:345{367,)j (1997.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF