Relativized Separations of Worst-Case and Average-Case Complexities for NP

  • Authors:

  • Russell Impagliazzo

  • Affiliations:

  • -

  • Venue:
  • CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
  • Year:
  • 2011

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Abstract

Non-relativization of complexity issues can beinterpreted as showing that these issues cannot be resolvedby "black-box" techniques. We show that the assumptionDistNP is contained in AvgP does not imply that NP =RP byrelativizing techniques. More precisely, we give an oraclerelative to which the assumption holds but the conclusionfails. Moreover, relative to our oracle, there are problems inthe intersection of NP and CoNP that require exponential circuit complexity.We also give an alternate version where DistNP is contained in AvgPis true, but a problem in the second level of the polynomialhierarchy is hard on the uniform distribution.