2011
DOI: 10.1007/s00037-011-0010-8
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Derandomizing Arthur-Merlin Games and Approximate Counting Implies Exponential-Size Lower Bounds

Abstract: Abstract. We show that if Arthur-Merlin protocols can be derandomized, then there is a language computable in deterministic exponentialtime with access to an NP oracle, that requires circuits of exponential size. More formally, if every promise problem in prAM, the class of promise problems that have Arthur-Merlin protocols, can be computed by a deterministic polynomial-time algorithm with access to an NP oracle then there is a language in E NP that requires circuits of size Ω(2 n /n). The lower bound in the c… Show more

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Cited by 11 publications
(4 citation statements)
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“…Derandomizations of prAM are also known to imply circuit lower bounds, which are stronger than what the aforementioned results give from derandomizations of prBPP in that they either yield exponentialsize bounds [38] or give lower bounds for nondeterministic circuits [39].…”
Section: Derandomization Vs Lower Boundsmentioning
confidence: 97%
“…Derandomizations of prAM are also known to imply circuit lower bounds, which are stronger than what the aforementioned results give from derandomizations of prBPP in that they either yield exponentialsize bounds [38] or give lower bounds for nondeterministic circuits [39].…”
Section: Derandomization Vs Lower Boundsmentioning
confidence: 97%
“…Typically, the constructed pseudorandom generator is not strong enough to recover the original derandomization assumption (e.g. [IKW02,KI04,AGHK11,KvMS12,Wil13]) but some results are known that establish exact equivalence between certain sorts of derandomizations and certain sorts of pseudorandom generators (see [AvM12]). Goldreich has followed another approach [Gol11a,Gol11b] to construct pseudorandom generators from derandomization assumptions in the BPP setting.…”
Section: Derandomization Vs Pseudorandom Generatorsmentioning
confidence: 99%
“…For example, it is shown in (Aaronson et al 2010;Aydınlıoǧlu et al 2011) that E prSBP contains sets of circuit complexity Ω(2 n /n).…”
Section: Definitionsmentioning
confidence: 99%