TY - JOUR

T1 - Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games

AU - Gutfreund, Dan

AU - Shaltiel, Ronen

AU - Ta-Shma, Amnon

PY - 2003

Y1 - 2003

N2 - Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap result" 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 sub-exponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm in the uniform average-case setting (i.e., it is infeasible to come up with inputs on which the algorithm fails). For the class AM ⊂ coAM we can remove the average-case clause and show under the same assumption that AM ⊂ coAM = NP ⊂ coNP. A new ingredient in our proof is identifying a novel resiliency property of hardness vs. randomness trade-offs. We observe that the Miltersen-Vinodchandran generator has this property.

AB - Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap result" 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 sub-exponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm in the uniform average-case setting (i.e., it is infeasible to come up with inputs on which the algorithm fails). For the class AM ⊂ coAM we can remove the average-case clause and show under the same assumption that AM ⊂ coAM = NP ⊂ coNP. A new ingredient in our proof is identifying a novel resiliency property of hardness vs. randomness trade-offs. We observe that the Miltersen-Vinodchandran generator has this property.

UR - http://www.scopus.com/inward/record.url?scp=0043016261&partnerID=8YFLogxK

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AN - SCOPUS:0043016261

SN - 1093-0159

SP - 33

EP - 47

JO - Proceedings of the Annual IEEE Conference on Computational Complexity

JF - Proceedings of the Annual IEEE Conference on Computational Complexity

T2 - 18th Annual IEEE Conference on Computational Complexity

Y2 - 7 July 2003 through 10 July 2003

ER -