Low-End Uniform Hardness versus Randomness Tradeoffs for AM

Impagliazzo and Wigderson proved a hardness versus randomness tradeoff for BPP in the uniform setting, which was subsequently extended to give optimal tradeoffs for the full range of possible hardness assumptions (in slightly weaker settings). In this work, the authors give uniform hardness versus randomness tradeoffs for AM that are near-optimal for the full range of possible hardness assumptions. Following Gutfreund, Shaltiel, and Ta-Shma, the authors do this by constructing a hitting-set-generator (HSG) for AM with "resilient reconstruction." The main new idea is to have the reconstruction procedure operate implicitly and locally on superpolynomially large objects, using tools from PCPs (low-degree testing, self-correction) together with a novel use of extractors that are built from Reed-Muller codes for a sort of locally computable error-reduction. (ProQuest: ... denotes formulae/symbols omitted.)