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On resource-bounded measure and pseudorandomness

  • V. Arvind
  • J. Köbler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1346)

Abstract

In this paper we extend a key result of Nisan and Wigderson [17] to the nondeterministic setting: for all α > 0 we show that if there is a language in E = DTIME(2O(n)) that is hard to approximate by nondeterministic circuits of size 2 αn , then there is a pseudorandom generator that can be used to derandomize BP·NP (in symbols, BP·NP = NP). By applying this extension we are able to answer some open questions in [14] regarding the derandomization of the classes BP·σ k P and BP·θ k P under plausible measure theoretic assumptions. As a consequence, if θ 2 P does not have p-measure 0, then AM ∩ coAM is low for θ 2 P . Thus, in this case, the graph isomorphism problem is low for θ 2 P . By using the Nisan-Wigderson design of a pseudorandom generator we unconditionally show the inclusion MA ⊑ ZPPNPNP and that MA∩ coMA is low for ZPPNP.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • V. Arvind
    • 1
  • J. Köbler
    • 2
  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Theoretische InformatikUniversitÄt UlmUlmGermany

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