Abstract

In this paper we extend a key result of Nisan and Wigderson [17] to the nondeterministic setting: for all ff ? 0 we show that if there is a language in E = DTIME(2 O(n) ) that is hard to approximate by nondeterministic circuits of size 2 ffn , then there is a pseudorandom generator that can be used to derandomize BP \Delta NP (in symbols, BP \Delta NP = NP). By applying this extension we are able to answer some open questions in [14] regarding the derandomization of the classes BP \Delta \Sigma P k and BP \Delta \Theta P k under plausible measure theoretic assumptions. As a consequence, if \Theta P 2 does not have p-measure 0, then AM " coAM is low for \Theta P 2 . Thus, in this case, the graph isomorphism problem is low for \Theta P 2 . By using the NisanWigderson design of a pseudorandom generator we unconditionally show the inclusion MA ` ZPP NP and that MA " coMA is low for ZPP NP . 1 Introduction In recent years, following the development of resource-bounded meas...

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