Worst-Case Vs. Algorithmic Average-Case Complexity in the Polynomial-Time Hierarchy

@inproceedings{Gutfreund2006WorstCaseVA,
  title={Worst-Case Vs. Algorithmic Average-Case Complexity in the Polynomial-Time Hierarchy},
  author={Dan Gutfreund},
  booktitle={APPROX-RANDOM},
  year={2006}
}
  • Dan Gutfreund
  • Published in APPROX-RANDOM 28 August 2006
  • Computer Science, Mathematics
We show that for every integer k>1, if Σk, the k'th level of the polynomial-time hierarchy, is worst-case hard for probabilistic polynomial-time algorithms, then there is a language L ∈Σk 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… 
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