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Explore three recent results utilizing obfuscation to address open questions in theoretical computer science. Delve into the areas of bounded arithmetic, derandomization, metacomplexity, average-case complexity, and differential privacy. Examine the Circuit Range Avoidance problem and its implications for separating Cook's theory PV1 from Jeřábek's theory APC1. Investigate the NP-hardness of computing conditional time-bounded Kolmogorov complexity and its connection to eliminating Heuristica. Discover a novel task in differential privacy that is achievable with a computational adversary but impossible with an all-powerful one. Gain insights into the applications of indistinguishability obfuscation, differing inputs obfuscation, and keyless collision-resistant hash functions in solving longstanding theoretical problems.
