TY - JOUR
T1 - In search of an easy witness
T2 - Exponential time vs. probabilistic polynomial time
AU - Impagliazzo, Russell
AU - Kabanets, Valentine
AU - Wigderson, Avi
PY - 2002/12
Y1 - 2002/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=23844442856&partnerID=8YFLogxK
U2 - 10.1016/S0022-0000(02)00024-7
DO - 10.1016/S0022-0000(02)00024-7
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AN - SCOPUS:23844442856
SN - 0022-0000
VL - 65
SP - 672
EP - 694
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
IS - 4
ER -