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b(ther)-5 b(e)32 b(is)e(a)h(quick)f(PR)n(G)g Fi(G)25 b Fw(:)h Ff(f)p Fw(0)p Fi(;)15 b Fw(1)p Ff(g)1888 2376 y Fg(n)1962 2409 y Ff(!)25 b(f)p Fw(0)p Fi(;)15 b Fw(1)p Ff(g)2298 2376 y Fg(m)2367 2409 y Fm(,)31 b(then)g(ther)-5 b(e)32 b(is)e(a)h Fw(2)3068 2376 y Fg(O)r Fs(\()p Fg(n)p Fs(\))3226 2409 y Fm(-time)f(c)-5 b(omputable)0 2522 y(Bo)g(ole)g(an)35 b(function)e Fi(f)h Fw(:)26 b Ff(f)p Fw(0)p Fi(;)15 b Fw(1)p Ff(g)1051 2489 y Fg(n)p Fs(+1)1215 2522 y Ff(!)25 b(f)p Fw(0)p Fi(;)15 b Fw(1)p Ff(g)35 b Fm(of)e(har)-5 b(dness)35 b Fi(m)p Fm(.)0 2709 y(Pr)-5 b(o)g(of.)47 b Fw(Consider)28 b(the)j(Bo)s(olean)g(function)e Fi(f)39 b Fw(de\014ned)29 b(as)i(follo)m(ws:)40 b(for)30 b(ev)m(ery)h Fi(x)25 b Ff(2)g(f)p Fw(0)p Fi(;)15 b Fw(1)p Ff(g)3132 2676 y Fg(n)p Fs(+1)3272 2709 y Fw(,)1115 2913 y Fi(f)10 b Fw(\()p Fi(x)p Fw(\))25 b(=)g(0)h Ff(,)f Fi(x)g Ff(2)g(f)p Fi(G)p Fw(\()p Fi(y)s Fw(\))1998 2927 y Fs(1)p Fg(::n)p Fs(+1)2236 2913 y Ff(j)g Fi(y)j Ff(2)d(f)p Fw(0)p Fi(;)15 b Fw(1)p Ff(g)2665 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b(T)-7 b(e)i(chnolo)g(gy)472 1866 y(and)30 b(The)-5 b(or)g(etic)g(al)31 b(Computer)f(Scienc)-5 b(e)p Fw(,)26 b(v)m(olume)g(1346)i(of)e Fm(L)-5 b(e)g(ctur)g(e)29 b(Notes)g(in)f(Computer)i(Scienc)-5 b(e)p Fw(,)472 1979 y(pages)31 b(235{249.)j(Springer)28 b(V)-8 b(erlag,)31 b(1997.)0 2164 y([AS97])213 b(S.)21 b(Arora)f(and)h(M.)g(Sudan.)i(Impro)m(v)m(ed)e(lo)m(w-degree)g(testing) g(and)f(its)g(applications.)j(In)d Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)472 2277 y(of)26 b(the)g(Twenty-Ninth)g(A)n(nnual)f(A)n(CM)f(Symp)-5 b(osium)27 b(on)f(The)-5 b(ory)27 b(of)f(Computing)p Fw(,)f(pages)f(485{495,)472 2390 y(1997.)0 2575 y([Bab85])172 b(L.)40 b(Babai.)70 b(T)-8 b(rading)38 b(group)i(theory)g(for)g (randomness.)68 b(In)39 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)44 b(of)d(the)h(Sevente)-5 b(enth)472 2688 y(A)n(nnual)33 b(A)n(CM)e(Symp)-5 b(osium)35 b(on)e(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)e(pages)g(421{429,)j(1985.)0 2874 y([BF90])209 b(D.)32 b(Bea)m(v)m(er)h(and)e(J.)g(F)-8 b(eigen)m(baum.)44 b(Hiding)29 b(instances)i(in)f(m)m(ultioracle)g (queries.)42 b(In)31 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)472 2986 y(of)29 b(the)f(Seventh)g(A)n(nnual)g(Symp)-5 b(osium)30 b(on)f(The)-5 b(or)g(etic)g(al)30 b(Asp)-5 b(e)g(cts)29 b(of)f(Computer)i(Scienc)-5 b(e)p Fw(,)26 b(v)m(olume)472 3099 y(415)31 b(of)f Fm(L)-5 b(e)g(ctur)g(e)33 b(Notes)f(in)g(Computer) h(Scienc)-5 b(e)p Fw(,)30 b(pages)g(37{48,)i(Berlin,)d(1990.)j (Springer)27 b(V)-8 b(erlag.)0 3285 y([BF99])209 b(H.)37 b(Buhrman)d(and)i(L.)g(F)-8 b(ortno)m(w.)59 b(One-sided)34 b(v)m(ersus)i(t)m(w)m(o-sided)g(error)g(in)e(probabilistic)f(com-)472 3398 y(putation.)80 b(In)43 b(C.)g(Meinel)g(and)g(S.)g(Tison,)j (editors,)h Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)47 b(of)e(the)g(Sixte)-5 b(enth)46 b(A)n(nnual)472 3510 y(Symp)-5 b(osium)33 b(on)e(The)-5 b(or)g(etic)g(al)33 b(Asp)-5 b(e)g(cts)31 b(of)g(Computer)g(Scienc)-5 b(e)p Fw(,)29 b(v)m(olume)f(1563)h(of)g Fm(L)-5 b(e)g(ctur)g(e)31 b(Notes)472 3623 y(in)i(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(pages)h(100{109.)j(Springer)28 b(V)-8 b(erlag,)31 b(1999.)0 3809 y([BFL91])152 b(L.)25 b(Babai,)i(L.)e(F)-8 b(ortno)m(w,)28 b(and)d(C.)g(Lund.)30 b(Non-deterministic)24 b(exp)s(onen)m(tial)g (time)h(has)g(t)m(w)m(o-pro)m(v)m(er)472 3922 y(in)m(teractiv)m(e)31 b(proto)s(cols.)41 b Fm(Computational)36 b(Complexity)p Fw(,)c(1:3{40,)h(1991.)0 4107 y([BFNW93])48 b(L.)41 b(Babai,)j(L.)d(F) -8 b(ortno)m(w,)45 b(N.)d(Nisan,)h(and)d(A.)h(Wigderson.)72 b(BPP)41 b(has)g(sub)s(exp)s(onen)m(tial)d(time)472 4220 y(sim)m(ulations)29 b(unless)f(EXPTIME)i(has)g(publishable)d(pro)s (ofs.)39 b Fm(Complexity)p Fw(,)33 b(3:307{318,)h(1993.)0 4405 y([BFT98])143 b(H.)28 b(Buhrman,)f(L.)h(F)-8 b(ortno)m(w,)30 b(and)d(L.)g(Thierauf.)34 b(Nonrelativizing)26 b(separations.)36 b(In)27 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)472 4518 y(of)31 b(the)h(Thirte)-5 b(enth)32 b(A)n(nnual)f(IEEE)f(Confer)-5 b(enc)g(e)32 b(on)f(Computational)j(Complexity)p Fw(,)d(pages)e(8{12,) 472 4631 y(1998.)0 4816 y([BH89])200 b(R.)32 b(Boppana)h(and)e(R.)i (Hirsc)m(hfeld.)44 b(Pseudo-random)31 b(generators)i(and)f(complexit)m (y)g(classes.)46 b(In)472 4929 y(S.)34 b(Micali,)g(editor,)g Fm(A)-5 b(dvanc)g(es)37 b(in)f(Computing)h(R)-5 b(ese)g(ar)g(ch)p Fw(,)37 b(v)m(olume)d(5,)h(pages)g(1{26.)h(JAI)d(Press,)472 5042 y(1989.)0 5227 y([BM84])185 b(M.)27 b(Blum)e(and)g(S.)h(Micali.)33 b(Ho)m(w)27 b(to)f(generate)i(cryptographically)d(strong)h(sequences)g (of)g(pseudo-)472 5340 y(random)k(bits.)39 b Fm(SIAM)32 b(Journal)i(on)f(Computing)p Fw(,)f(13:850{864,)i(1984.)p eop %%Page: 14 14 14 13 bop 0 91 a Fw([BM88])185 b(L.)43 b(Babai)g(and)f(S.)h(Moran.)78 b(Arth)m(ur-Merlin)40 b(games:)67 b(a)43 b(randomized)f(pro)s(of)g (system,)k(and)d(a)472 204 y(hierarc)m(h)m(y)c(of)g(complexit)m(y)g (classes.)67 b Fm(Journal)42 b(of)f(Computer)h(and)f(System)h(Scienc)-5 b(es)p Fw(,)41 b(36:254{)472 317 y(276,)32 b(1988.)0 504 y([CNS99])147 b(J.-Y.)30 b(Cai,)e(A.)i(Nerurk)-5 b(ar,)28 b(and)h(D.)g(Siv)-5 b(akumar.)37 b(Hardness)28 b(and)g(hierarc)m(h)m(y)h(theorems)g(for)g(prob-)472 617 y(abilistic)g(quasi-p)s(olynomial)f(time.)43 b(In)30 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)35 b(of)f(the)g(Thirty-First)h(A)n (nnual)e(A)n(CM)f(Sym-)472 730 y(p)-5 b(osium)34 b(on)f(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(pages)f(726{735,)j(1999.)0 916 y([CR)-8 b(T98])141 b(A.E.F.)43 b(Clemen)m(ti,)g(J.D.P)-8 b(.)42 b(Rolim,)h(and)d(L.)i(T)-8 b(revisan.)72 b(Recen)m(t)42 b(adv)-5 b(ances)42 b(to)m(w)m(ards)g(pro)m(ving)472 1029 y(P=BPP.)96 b Fm(Bul)5 b(letin)50 b(of)g(the)g(Eur)-5 b(op)g(e)g(an)52 b(Asso)-5 b(ciation)51 b(for)g(The)-5 b(or)g(etic)g(al)52 b(Computer)f(Scienc)-5 b(e)p Fw(,)472 1142 y(\(64\):96{103,)35 b(F)-8 b(ebruary)31 b(1998.)0 1329 y([F)-8 b(or01])200 b(L.)25 b(F)-8 b(ortno)m(w.)32 b(Comparing)23 b(notions)h(of)g(full)e(derandomization.)30 b(In)24 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)29 b(of)e(the)h(Sixte)-5 b(enth)472 1442 y(A)n(nnual)33 b(IEEE)e(Confer)-5 b(enc)g(e)34 b(on)f(Computational)i(Complexity)p Fw(,)e(pages)e(28{34,)i(2001.)0 1628 y([GKL88])133 b(O.)30 b(Goldreic)m(h,)f(H.)i(Kra)m(w)m(czyk,)g (and)e(M.)i(Lub)m(y)-8 b(.)39 b(On)30 b(the)g(existence)g(of)g (pseudo-random)f(genera-)472 1741 y(tors.)41 b(In)30 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)35 b(of)e(the)g(Twenty-Ninth)g(A)n (nnual)f(IEEE)g(Symp)-5 b(osium)34 b(on)g(F)-7 b(oundations)35 b(of)472 1854 y(Computer)f(Scienc)-5 b(e)p Fw(,)30 b(pages)h(12{24,)i (1988.)0 2041 y([GL89])204 b(O.)43 b(Goldreic)m(h)f(and)g(L.A.)h (Levin.)76 b(A)42 b(hard-core)h(predicate)g(for)f(all)g(one-w)m(a)m(y)i (functions.)76 b(In)472 2153 y Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)44 b(of)d(the)h(Twenty-First)h(A)n(nnual)e(A)n(CM)f(Symp)-5 b(osium)43 b(on)f(The)-5 b(ory)43 b(of)f(Computing)p Fw(,)472 2266 y(pages)31 b(25{32,)i(1989.)0 2453 y([GMW91])85 b(O.)27 b(Goldreic)m(h,)g(S.)g(Micali,)f(and)h(A.)g(Wigderson.)34 b(Pro)s(ofs)27 b(that)g(yield)e(nothing)h(but)h(their)f(v)-5 b(alidit)m(y)472 2566 y(or)31 b(all)f(languages)i(in)d(NP)i(ha)m(v)m(e) i(zero-kno)m(wledge)f(pro)s(of)e(systems.)43 b Fm(Journal)34 b(of)g(the)f(Asso)-5 b(ciation)472 2679 y(for)33 b(Computing)h (Machinery)p Fw(,)d(38:691{729,)k(1991.)0 2865 y([GNW95])100 b(O.)31 b(Goldreic)m(h,)f(N.)h(Nisan,)g(and)f(A.)h(Wigderson.)41 b(On)30 b(Yao's)i(X)m(OR-Lemma.)42 b Fm(Ele)-5 b(ctr)g(onic)34 b(Col)5 b(lo-)472 2978 y(quium)32 b(on)h(Computational)j(Complexity)p Fw(,)c(TR95-050,)h(1995.)0 3165 y([GS89])210 b(S.)41 b(Goldw)m(asser)f(and)g(M.)h(Sipser.)69 b(Priv)-5 b(ate)41 b(coins)f(v)m(ersus)g(public)e(coins)i(in)f(in)m(teractiv)m(e)j(pro)s (of)472 3278 y(systems.)35 b(In)26 b(S.)g(Micali,)h(editor,)g Fm(A)-5 b(dvanc)g(es)30 b(in)f(Computing)h(R)-5 b(ese)g(ar)g(ch)p Fw(,)30 b(v)m(olume)c(5,)i(pages)f(73{90.)472 3391 y(JAI)j(Press,)g (1989.)0 3577 y([GVW00])100 b(O.)21 b(Goldreic)m(h,)i(S.)e(V)-8 b(adhan,)23 b(and)e(A.)h(Wigderson.)j(Simpli\014ed)17 b(derandomization)j(of)h(BPP)h(using)e(a)472 3690 y(hitting)27 b(set)i(generator.)39 b Fm(Ele)-5 b(ctr)g(onic)31 b(Col)5 b(lo)-5 b(quium)32 b(on)f(Computational)j(Complexity)p Fw(,)d(TR00-004,)472 3803 y(2000.)0 3990 y([GW99])168 b(O.)27 b(Goldreic)m(h)f(and)h(A.)g(Wigderson.)35 b(Impro)m(v)m(ed)27 b(derandomization)f(of)h(BPP)h(using)d(a)j(hitting)d(set)472 4103 y(generator.)k(In)22 b(D.)i(Ho)s(c)m(h)m(baum,)g(K.)f(Jansen,)h (J.D.P)-8 b(.)23 b(Rolim,)g(and)g(A.)g(Sinclair,)e(editors,)j Fm(R)-5 b(andom-)472 4216 y(ization,)28 b(Appr)-5 b(oximation,)30 b(and)c(Combinatorial)i(Optimization)p Fw(,)e(v)m(olume)c(1671)i(of)f Fm(L)-5 b(e)g(ctur)g(e)26 b(Notes)472 4329 y(in)g(Computer)h(Scienc)-5 b(e)p Fw(,)25 b(pages)e(131{137.)k(Springer)20 b(V)-8 b(erlag,)26 b(1999.)k(\(RANDOM-APPR)m(O)m(X'99\).)0 4515 y([GZ97])205 b(O.)28 b(Goldreic)m(h)f(and)g(D.)i(Zuc)m(k)m(erman.)36 b(Another)28 b(pro)s(of)f(that)i(BPP)p Ff(\022)p Fw(PH)e(\(and)h (more\).)37 b Fm(Ele)-5 b(ctr)g(onic)472 4628 y(Col)5 b(lo)-5 b(quium)34 b(on)f(Computational)j(Complexity)p Fw(,)c(TR97-045,)h(1997.)0 4815 y([HILL99])117 b(J.)36 b(H)-11 b(\027)-57 b(astad,)38 b(R.)e(Impagliazzo,)h(L.)f(Levin,)g(and) f(M.)h(Lub)m(y)-8 b(.)57 b(A)35 b(pseudorandom)g(generator)h(from)472 4928 y(an)m(y)31 b(one-w)m(a)m(y)h(function.)39 b Fm(SIAM)32 b(Journal)i(on)f(Computing)p Fw(,)e(28:1364{1396,)36 b(1999.)0 5114 y([IKW01])135 b(R.)32 b(Impagliazzo,)h(V.)f(Kabanets,)g (and)f(A.)i(Wigderson.)44 b(In)31 b(searc)m(h)h(of)g(an)g(easy)g (witness:)42 b(Exp)s(o-)472 5227 y(nen)m(tial)31 b(time)g(vs.)h (probabilistic)c(p)s(olynomial)g(time.)44 b(In)31 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)35 b(of)f(the)g(Sixte)-5 b(enth)35 b(A)n(nnual)472 5340 y(IEEE)d(Confer)-5 b(enc)g(e)33 b(on)g(Computational)j(Complexity)p Fw(,)c(pages)f(1{11,)i(2001.)p eop %%Page: 15 15 15 14 bop 0 91 a Fw([Imp95])172 b(R.)25 b(Impagliazzo.)32 b(Hard-core)26 b(distributions)21 b(for)k(somewhat)g(hard)f(problems.) 30 b(In)24 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)30 b(of)472 204 y(the)g(Thirty-Sixth)h(A)n(nnual)e(IEEE)f(Symp)-5 b(osium)32 b(on)e(F)-7 b(oundations)31 b(of)f(Computer)h(Scienc)-5 b(e)p Fw(,)27 b(pages)472 317 y(538{545,)34 b(1995.)0 505 y([ISW99])155 b(R.)36 b(Impagliazzo,)i(R.)e(Shaltiel,)f(and)h(A.)g (Wigderson.)56 b(Near-optimal)36 b(con)m(v)m(ersion)g(of)g(hardness)472 618 y(in)m(to)g(pseudo-randomness.)54 b(In)34 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)40 b(of)d(the)h(F)-7 b(ortieth)39 b(A)n(nnual)e(IEEE)f(Symp)-5 b(osium)39 b(on)472 731 y(F)-7 b(oundations)35 b(of)e(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(pages)h(181{190,)j(1999.)0 918 y([ISW00])155 b(R.)40 b(Impagliazzo,)i(R.)e(Shaltiel,)f(and)g(A.)h(Wigderson.)67 b(Extractors)41 b(and)d(pseudorandom)g(gen-)472 1031 y(erators)h(with)e(optimal)g(seed)i(length.)63 b(In)37 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)42 b(of)e(the)h(Thirty-Se)-5 b(c)g(ond)41 b(A)n(nnual)f(A)n(CM)472 1144 y(Symp)-5 b(osium)35 b(on)e(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(pages)f(1{10,)h(2000.)0 1332 y([IW97])206 b(R.)33 b(Impagliazzo)g(and)f(A.)h(Wigderson.)47 b(P=BPP)32 b(if)g(E)g (requires)g(exp)s(onen)m(tial)f(circuits:)44 b(Deran-)472 1445 y(domizing)29 b(the)h(X)m(OR)h(Lemma.)40 b(In)29 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)35 b(of)e(the)f(Twenty-Ninth)h(A)n (nnual)f(A)n(CM)g(Symp)-5 b(o-)472 1557 y(sium)33 b(on)g(The)-5 b(ory)34 b(of)f(Computing)p Fw(,)f(pages)f(220{229,)i(1997.)0 1745 y([IW98])206 b(R.)35 b(Impagliazzo)g(and)g(A.)g(Wigderson.)54 b(Randomness)34 b(vs.)h(time:)50 b(De-randomization)35 b(under)f(a)472 1858 y(uniform)d(assumption.)45 b(In)32 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)37 b(of)e(the)g(Thirty-Ninth)h(A)n (nnual)e(IEEE)g(Symp)-5 b(osium)36 b(on)472 1971 y(F)-7 b(oundations)35 b(of)e(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(pages)h(734{743,)j(1998.)0 2159 y([Kab00])165 b(V.)28 b(Kabanets.)35 b(Easiness)26 b(assumptions)f(and)i(hardness)e(tests:)40 b(Trading)26 b(time)g(for)h(zero)h(error.)35 b(In)472 2271 y Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)40 b(of)e(the)g(Fifte)-5 b(enth)39 b(A)n(nnual)e(IEEE)g(Confer)-5 b(enc)g(e)38 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b(ctr)g(onic)34 b(Col)5 b(lo)-5 b(quium)33 b(on)g(Computational)j(Complexity)p Fw(,)c(TR00-034,)h(2000.)0 3587 y([Lev87])187 b(L.A.)59 b(Levin.)122 b(One-w)m(a)m(y)59 b(functions)d(and)i(pseudorandom)e (generators.)124 b Fm(Combinatoric)-5 b(a)p Fw(,)472 3699 y(7\(4\):357{363,)36 b(1987.)0 3887 y([Lip91])198 b(R.)48 b(Lipton.)90 b(New)48 b(directions)e(in)g(testing.)91 b(In)47 b(J.)g(F)-8 b(eigen)m(baum)48 b(and)f(M.)h(Merrit,)j(editors,) 472 4000 y Fm(Distribute)-5 b(d)37 b(Computing)g(and)f(Crypto)-5 b(gr)g(aphy)p Fw(,)39 b(pages)c(191{202.)i(DIMA)m(CS)e(Series)e(in)f (Discrete)472 4113 y(Mathematics)g(and)d(Theoretical)h(Computer)g (Science,)g(V)-8 b(olume)31 b(2,)g(AMS,)f(1991.)0 4301 y([Lu00])224 b(C.-J.)25 b(Lu.)31 b(Derandomizing)23 b(Arth)m(ur-Merlin) g(games)i(under)e(uniform)g(assumptions.)29 b(In)24 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(d-)472 4413 y(ings)30 b(of)h(the)f(Eleventh) h(A)n(nnual)f(International)i(Symp)-5 b(osium)32 b(on)f(A)n(lgorithms)g (and)h(Computation)472 4526 y(\(ISAA)n(C'00\))p Fw(,)f(2000.)0 4714 y([Mil01])197 b(P)-8 b(.B.)44 b(Miltersen.)76 b(Derandomizing)42 b(complexit)m(y)g(classes.)77 b(In)42 b(S.)g(Ra)5 b(jasek)-5 b(aran)44 b(P)-8 b(.)43 b(P)m(ardalos,)472 4827 y(J.)29 b(Reif,)f(and)g(J.)g(Rolim,)g(editors,)g Fm(Handb)-5 b(o)g(ok)33 b(of)e(R)-5 b(andomize)g(d)34 b(Computing)p Fw(,)c(v)m(olume)e(I)s(I.)g(Klu)m(w)m(er)472 4940 y(Academic)j (Publishers,)c(2001.)42 b(\(a)32 b(draft)e(is)f(a)m(v)-5 b(ailable)30 b(at)h Fu(www.brics.dk/)p Ff(\030)p Fu(bromille)p Fw(\).)0 5127 y([MR95])182 b(R.)34 b(Mot)m(w)m(ani)h(and)f(P)-8 b(.)34 b(Ragha)m(v)-5 b(an.)53 b Fm(R)-5 b(andomize)g(d)39 b(A)n(lgorithms)p Fw(.)53 b(Cam)m(bridge)33 b(Univ)m(ersit)m(y)g (Press,)472 5240 y(New)e(Y)-8 b(ork,)31 b(1995.)p eop %%Page: 16 16 16 15 bop 0 91 a Fw([MV99])181 b(P)-8 b(.B.)37 b(Miltersen)d(and)i (N.V.)g(Vino)s(dc)m(handran.)54 b(Derandomizing)35 b(Arth)m(ur-Merlin)e (games)j(using)472 204 y(hitting)d(sets.)53 b(In)34 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)38 b(of)f(the)f(F)-7 b(ortieth)38 b(A)n(nnual)e(IEEE)g(Symp)-5 b(osium)38 b(on)f(F)-7 b(oundations)472 317 y(of)33 b(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(pages)h(71{80,)i(1999.)0 505 y([Nis91])202 b(N.)26 b(Nisan.)33 b(Pseudo)25 b(random)g(bits)g(for)h(constan)m(t)h (depth)e(circuits.)32 b Fm(Combinatoric)-5 b(a)p Fw(,)29 b(11\(1\):63{70,)472 618 y(1991.)0 805 y([NW94])171 b(N.)44 b(Nisan)e(and)g(A.)i(Wigderson.)78 b(Hardness)42 b(vs.)h(randomness.)77 b Fm(Journal)46 b(of)e(Computer)i(and)472 918 y(System)34 b(Scienc)-5 b(es)p Fw(,)30 b(49:149{167,)35 b(1994.)0 1106 y([Plo60])199 b(M.)44 b(Plotkin.)79 b(Binary)43 b(co)s(des)h(with)e(sp)s(eci\014ed)g(minim)m(um)f(distance.)80 b Fm(IRE)45 b(T)-7 b(r)i(ansactions)47 b(on)472 1219 y(Information)35 b(The)-5 b(ory)p Fw(,)32 b(6:445{450,)j(1960.)0 1406 y([RR99])198 b(R.)42 b(Raz)g(and)f(O.)g(Reingold.)72 b(On)41 b(recycling)g(the)g(randomness)g(of)g(states)i(in)d(space)i(b)s (ounded)472 1519 y(computation.)53 b(In)34 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)38 b(of)e(the)h(Thirty-First)h(A)n(nnual)e(A)n (CM)f(Symp)-5 b(osium)39 b(on)d(The)-5 b(ory)472 1632 y(of)33 b(Computing)p Fw(,)f(pages)f(168{178,)i(1999.)0 1820 y([Sha81])185 b(A.)25 b(Shamir.)j(On)23 b(the)i(generation)f(of)g (cryptographically)f(strong)h(pseudo-random)f(sequences.)31 b(In)472 1933 y Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)32 b(of)d(the)h (Eighth)g(International)i(Col)5 b(lo)-5 b(quium)30 b(on)g(A)n(utomata,) h(L)-5 b(anguages,)30 b(and)h(Pr)-5 b(o-)472 2046 y(gr)g(amming)p Fw(,)36 b(v)m(olume)c(62)i(of)f Fm(L)-5 b(e)g(ctur)g(e)36 b(Notes)f(in)g(Computer)i(Scienc)-5 b(e)p Fw(,)33 b(pages)h(544{550.)i (Springer)472 2159 y(V)-8 b(erlag,)32 b(1981.)0 2346 y([STV01])147 b(M.)36 b(Sudan,)g(L.)g(T)-8 b(revisan,)36 b(and)f(S.)g(V)-8 b(adhan.)56 b(Pseudorandom)35 b(generators)h(without) f(the)h(X)m(OR)472 2459 y(lemma.)44 b Fm(Journal)34 b(of)g(Computer)h (and)g(System)f(Scienc)-5 b(es)p Fw(,)32 b(62\(2\):236{266,)37 b(2001.)46 b(\(preliminary)472 2572 y(v)m(ersion)30 b(in)f(STOC'99\).)0 2760 y([SU01])213 b(R.)33 b(Shaltiel)e(and)h(C.)g(Umans.)47 b(Simple)31 b(extractors)j(for)e(all)g(min-en)m(tropies)f(and)h(a)h (new)f(pseudo-)472 2873 y(random)39 b(generator.)69 b(In)39 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)43 b(of)e(the)g(F)-7 b(orty-Se)i(c)g(ond)44 b(A)n(nnual)d(IEEE)e(Symp)-5 b(osium)43 b(on)472 2985 y(F)-7 b(oundations)35 b(of)e(Computer)h(Scienc)-5 b(e)p Fw(,)30 b(pages)h(648{657,)j(2001.)0 3173 y([Sud97])179 b(M.)22 b(Sudan.)j(Deco)s(ding)c(of)h(Reed)g(Solomon)f(co)s(des)g(b)s (ey)m(ond)g(the)h(error-correction)g(b)s(ound.)i Fm(Journal)472 3286 y(of)33 b(Complexity)p Fw(,)f(13\(1\):180{193,)k(1997.)0 3474 y([Sud00])179 b(M.)30 b(Sudan.)37 b(List)29 b(deco)s(ding:)39 b(Algorithms)27 b(and)i(applications.)37 b(In)29 b(J.)g(v)-5 b(an)29 b(Leeu)m(w)m(en,)h(O.)f(W)-8 b(atan-)472 3587 y(ab)s(e,)47 b(M.)d(Hagiy)m(a,)49 b(P)-8 b(.D.)45 b(Mosses,)j(and)43 b(T.)g(Ito,)48 b(editors,)e Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)47 b(of)e(the)h(International)472 3699 y(Confer)-5 b(enc)g(e)32 b(IFIP)e(TCS)h(2000)p Fw(,)f(v)m(olume)e(1872)i(of)e Fm(L)-5 b(e)g(ctur)g(e)31 b(Notes)g(in)f(Computer)i(Scienc)-5 b(e)p Fw(,)28 b(pages)472 3812 y(25{41.)33 b(Springer)28 b(V)-8 b(erlag,)32 b(August)e(2000.)0 4000 y([T)-8 b(o)s(d91])175 b(S.)25 b(T)-8 b(o)s(da.)32 b(PP)25 b(is)f(as)h(hard)f(as)h(the)g(p)s (olynomial-time)e(hierarc)m(h)m(y)-8 b(.)32 b Fm(SIAM)27 b(Journal)h(on)h(Computing)p Fw(,)472 4113 y(20\(5\):865{877,)36 b(1991.)0 4301 y([T)-8 b(re99])198 b(L.)25 b(T)-8 b(revisan.)31 b(Construction)24 b(of)i(extractors)g(using)e(pseudorandom)f (generators.)33 b(In)25 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)472 4413 y(of)32 b(the)h(Thirty-First)g(A)n(nnual)f(A)n(CM)e(Symp)-5 b(osium)34 b(on)f(The)-5 b(ory)33 b(of)f(Computing)p Fw(,)f(pages)g(141{148,)472 4526 y(1999.)0 4714 y([TSZS01])108 b(A.)42 b(T)-8 b(a-Shma,)45 b(D.)d(Zuc)m(k)m(erman,)j(and)c(S.)g (Safra.)74 b(Extractors)43 b(from)e(Reed-Muller)f(co)s(des.)75 b(In)472 4827 y Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)29 b(of)e(the)h(F)-7 b(orty-Se)i(c)g(ond)29 b(A)n(nnual)e(IEEE)f(Symp)-5 b(osium)29 b(on)e(F)-7 b(oundations)29 b(of)f(Computer)472 4940 y(Scienc)-5 b(e)p Fw(,)31 b(2001.)0 5127 y([Uma01])143 b(C.)43 b(Umans.)80 b(Pseudo-random)42 b(generators)j(for)e(all)f (hardnesses.)79 b(man)m(uscript)42 b(\(submitted\),)472 5240 y(No)m(v)m(em)m(b)s(er)32 b(2001.)p eop %%Page: 17 17 17 16 bop 0 91 a Fw([V)-8 b(al79])201 b(L.)22 b(V)-8 b(alian)m(t.)27 b(The)22 b(complexit)m(y)f(of)h(computing)f(the)h(p)s (ermanen)m(t.)27 b Fm(The)-5 b(or)g(etic)g(al)27 b(Computer)f(Scienc)-5 b(e)p Fw(,)472 204 y(8:189{201,)35 b(1979.)0 392 y([VV86])196 b(L.)36 b(V)-8 b(alian)m(t)36 b(and)f(V.)h(V)-8 b(azirani.)56 b(NP)36 b(is)e(as)i(easy)h(as)e(detecting)i(unique)d(solutions.)54 b Fm(The)-5 b(or)g(etic)g(al)472 505 y(Computer)34 b(Scienc)-5 b(e)p Fw(,)30 b(47:85{93,)k(1986.)0 692 y([Y)-8 b(ao82])182 b(A.C.)24 b(Y)-8 b(ao.)30 b(Theory)22 b(and)h(applications)e(of)j(trap) s(do)s(or)e(functions.)27 b(In)22 b Fm(Pr)-5 b(o)g(c)g(e)g(e)g(dings)28 b(of)e(the)h(Twenty-)472 805 y(Thir)-5 b(d)44 b(A)n(nnual)e(IEEE)f (Symp)-5 b(osium)44 b(on)f(F)-7 b(oundations)44 b(of)e(Computer)i (Scienc)-5 b(e)p Fw(,)43 b(pages)e(80{91,)472 918 y(1982.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF