Tales of Obfuscation in Bounded Arithmetic, Metacomplexity, and Differential Privacy

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.