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...

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Ronen Shaltiel, Christopher Umans
• Keywords: Algorithms, Arthur-Merlin Games, Possible Hardness Assumptions, STOC 2007, Uniform Hardness Vs