Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games

CC
CCC
2003
18th Annual IEEE Conference on Computational Complexity (CCC'03)
Abstract - Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games

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18th Annual IEEE Conference on Computational Complexity (CCC'03)

Aarhus, Denmark

July 07-July 10

ISBN: 0-7695-1879-6

	ASCII Text	x
	Dan Gutfreund, "Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games," Computational Complexity, Annual IEEE Conference on, pp. 33, 18th Annual IEEE Conference on Computational Complexity (CCC'03), 2003.

	BibTex	x
	@article{ 10.1109/CCC.2003.1214408, author = {Dan Gutfreund}, title = {Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games}, journal ={Computational Complexity, Annual IEEE Conference on}, volume = {0}, year = {2003}, issn = {1093-0159}, pages = {33}, doi = {http://doi.ieeecomputersociety.org/10.1109/CCC.2003.1214408}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Computational Complexity, Annual IEEE Conference on TI - Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games SN - 1093-0159 SP EP A1 - Dan Gutfreund, PY - 2003 KW - null VL - 0 JA - Computational Complexity, Annual IEEE Conference on ER -

Dan Gutfreund, The Hebrew University of Jerusalem, Israel, 91904

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2003.1214408

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 (^2O(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 nondeter- ministic 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 n coAM we can re- move the average-case clause and show under the same assumption that AM n coAM = NPncoNP. 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.

Citation:

Dan Gutfreund, "Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games," ccc, pp.33, 18th Annual IEEE Conference on Computational Complexity (CCC'03), 2003

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