In Search of an Easy Witness: Exponential Time vs. Probabilistic Polynomial Time

  • Authors:
  • Russell Impagliazzo;Valentine Kabanets;Avi Wigderson

  • Affiliations:
  • -;-;-

  • Venue:
  • CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
  • Year:
  • 2001

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Abstract

Institute for Advanced StudyAbstract: Restricting the search space {0,1}n to the set of truth tables of "easy" Boolean functions on log n variables, as well as using some known hardness-randomness tradeoffs, we establish a number of results relating the complexity of exponential-time and probabilistic polynomial-time complexity classes. In particular, we show that NEXP \subset P/poly \iff NEXP = MA; this can be interpreted to say that no derandomization of MA (and, hence, of promise-BPP) is possible unless NEXP contains a hard Boolean function. We also prove several downward closure results for ZPP, RP, BPP, and MA; e.g., we show EXP = BPP \iff EE = BPE, where EE is the double-exponential time class and BPE is the exponential-time analogue of BPP.