In Search of an Easy Witness: Exponential Time vs. Probabilistic Polynomial Time
| Citations: | 44 - 3 self |
BibTeX
@MISC{Impagliazzo_insearch,
author = {Russell Impagliazzo and Valentine Kabanets and Avi Wigderson},
title = {In Search of an Easy Witness: Exponential Time vs. Probabilistic Polynomial Time},
year = {}
}
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Abstract
Restricting the search space f0; 1g 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 polynomialtime complexity classes. In particular, we show that NEXP ae P=poly , NEXP = MA; this can be interpreted as saying 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 , EE = BPE, where EE is the double-exponential time class and BPE is the exponential-time analogue of BPP.
