Chain, Generalization of Covering Code, and Deterministic Algorithm for k-SAT

04/21/2018

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by   Sixue Liu, et al.

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We present the current fastest deterministic algorithm for k-SAT, improving the upper bound (2-2/k)^n + o(n) due to Moser and Scheder in STOC 2011. The algorithm combines a branching algorithm with the derandomized local search, whose analysis relies on a special sequence of clauses called chain, and a generalization of covering code based on linear programming. We also provide a more intelligent branching algorithm for 3-SAT to establish the upper bound 1.32793^n, improved from 1.3303^n.