In search of an easy witness: exponential time vs. probabilistic polynomial time

Russell Impagliazzo, Valentine Kabanets, Avi Wigderson
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
Restricting the search space f0; 1g 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 polynomialtime complexity classes. In particular, we show that NEXPCP=poly3NEXP ¼ 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
more &raquo; ... on. We also prove several downward closure results for ZPP, RP, BPP, and MA; e.g., we show EXP ¼ BPP3EE ¼ BPE, where EE is the double-exponential time class and BPE is the exponential-time analogue of BPP: r
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/s0022-0000(02)00024-7</a> <a target="_blank" rel="external noopener" href="">fatcat:lvshl4tmdrbnlaqly4ejcoarri</a> </span>
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