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Abstract

We show that for every integer k>1, if Σ k , the k’th level of the polynomial-time hierarchy, is worst-case hard for probabilistic polynomial-time algorithms, then there is a language L ∈Σ k such that for every probabilistic polynomial-time algorithm that attempts to decide it, there is a samplable distribution over the instances of L, on which the algorithm errs with probability at least 1/2–1/poly(n) (where the probability is over the choice of instances and the randomness of the algorithm). In other words, on this distribution the algorithm essentially does not perform any better than the algorithm that simply decides according to the outcome of an unbiased coin toss.

Keywords

Samplable Distribution Search Problem Boolean Formula Satisfying Assignment Random Coin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dan Gutfreund
    • 1
  1. 1.Division of Engineering and Applied SciencesHarvard UniversityCambridgeUSA

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