@article{7f9b07c1755140908cb1cdcbbd4b146c,
title = "Uniform hardness versus randomness tradeoffs for Arthur-Merlin games",
abstract = "Impagliazzo and Wigderson proved a uniform hardness vs. randomness {"}gap theorem{"} for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in E = DTIME(2 O(n)) can be proved to a subexponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm such that it is infeasible to come up with inputs on which the algorithm fails. We also show that if Arthur-Merlin protocols are not very strong (in the sense explained above) then AM ∩ coAM = NP ∩ coNP. Our technique combines the nonuniform hardness versus randomness tradeoff of Miltersen and Vinodchandran with {"}instance checking{"}. A key ingredient in our proof is identifying a novel {"}resilience{"} property of hardness vs. randomness tradeoffs.",
keywords = "Arthur-Merlin games, Derandomization",
author = "Dan Gutfreund and Ronen Shaltiel and Amnon Ta-Shma",
note = "Funding Information: The first author is supported in part by the Leibniz Center, the Israel Foundation of Science, a US-Israel Binational research grant, and an EU Information Technologies grant (IST-FP5). The second author is supported by the Koshland Scholarship.",
year = "2003",
doi = "10.1007/s00037-003-0178-7",
language = "אנגלית",
volume = "12",
pages = "85--130",
journal = "Computational Complexity",
issn = "1016-3328",
publisher = "Birkhauser Verlag Basel",
number = "3-4",
}