A Faster Clause-Shortening Algorithm for SAT with No Restriction on Clause Length

Abstract

We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. This algorithm uses the clause-shortening approach proposed by Schuler. The running time of the algorithm is O(2^(n(1−1/α))) where α = ln(m/n) + O(ln ln m) and n, m are respectively the number of variables and the number of clauses in the input formula. This bound is asymptotically better than the previously best known 2^(n(1−1/ log(2m))) bound for SAT.