We propose a new family of circuit-based sampling tasks, such that non-trivial algorithmic solutions to certain tasks from this family imply frontier uniform lower bounds such as ``NP is not in uniform ACC^0" and ``NP does not have uniform polynomial-size depth-two threshold circuits". Indeed, the most general versions of our ... more >>>

We prove that a $O(k \log k)$-probe local algorithm for $k$-Missing String presented by Vyas and Williams is asymptotically optimal among a certain class of algorithms for this problem. The best lower bound we are aware of for the general case is still $\Omega(k)$.

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Strong (resp. weak) average-case hardness refers to the properties of a computational problem in which a large (resp. small) fraction of instances are hard to solve. We develop a general framework for proving hardness self-amplification, that is, the equivalence between strong and weak average-case hardness. Using this framework, we prove ... more >>>