• DOI:10.1007/11830924_36
• Corpus ID: 14490408

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 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.