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

Russell Impagliazzo, Valentine Kabanets*, Avi Wigderson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

156 Scopus citations

Abstract

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 ⊂ 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.

Original languageEnglish
Pages (from-to)672-694
Number of pages23
JournalJournal of Computer and System Sciences
Volume65
Issue number4
DOIs
StatePublished - Dec 2002

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