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2007
ACM

Low-end uniform hardness vs. randomness tradeoffs for AM

14 years 3 months ago
Low-end uniform hardness vs. randomness tradeoffs for AM
In 1998, Impagliazzo and Wigderson [IW98] proved a hardness vs. randomness tradeoff for BPP in the uniform setting, which was subsequently extended to give optimal tradeoffs for the full range of possible hardness assumptions by Trevisan and Vadhan [TV02] (in a slightly weaker setting). In 2003, Gutfreund, Shaltiel and Ta-Shma [GSTS03] proved a uniform hardness vs. randomness tradeoff for AM, but that result only worked on the "high-end" of possible hardness assumptions. In this work, we give uniform hardness vs. randomness tradeoffs for AM that are near-optimal for the full range of possible hardness assumptions. Following [GSTS03], we do this by constructing a hittingset-generator (HSG) for AM with "resilient reconstruction." Our construction is a recursive variant of the Miltersen-Vinodchandran HSG [MV05], the only known HSG construction with this required property. The main new idea is to have the reconstruction procedure operate implicitly and locally on super...
Ronen Shaltiel, Christopher Umans
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2007
Where STOC
Authors Ronen Shaltiel, Christopher Umans
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