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

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 polynomialtime 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.

• Type: Conference
• Year: 2001
• Where: COCO
• Authors: Russell Impagliazzo, Valentine Kabanets, Avi Wigderson
• Keywords: Algorithms, Boolean Function, COCO 2001, Hard Boolean Function, Probabilistic Polynomialtime Complexity