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Speaker: Li-Yang Tan, ITT Chicago

Title: Derandomized search for CNF satisfying assignments in almost polynomial time

Abstract:

We consider the fundamental derandomization problem of deterministically finding a satisfying assignment to a CNF formula that has many satisfying assignments. We give a deterministic algorithm which, given an n-variable poly(n)-clause CNF formula F that has |F^{-1}(1)| \geq \eps 2^n, runs in time n^{\tilde{O}(\log\log n)^2} for \eps \ge 1/\polylog(n) and outputs a satisfying assignment of F. Prior to our work the fastest known algorithm for this problem was simply to enumerate over all seeds of a pseudorandom generator for CNFs; using the best known PRGs for CNFs [DETT10], this takes time n^{\tilde{\Omega}(\log n)} even for constant \eps.

Joint work with Rocco Servedio.