Algorithms for SAT Based on Search in Hamming Balls

Abstract

We present two simple algorithms for SAT and prove upper bounds on their running time. Given a Boolean formula F in conjunctive normal form, the first algorithm finds a satisfying assignment for F (if any) by repeating the following: Choose an assignment A at random and search for a satisfying assignment inside a Hamming ball around A (the radius of the ball depends on F). We show that this algorithm solves SAT with a small probability of error in at most 2$^{n - 0.712\sqrt{n}}$ steps, where n is the number of variables in F. To derandomize this algorithm, we use covering codes instead of random assignments. The deterministic algorithm solves SAT in at most 2$^{n - 2\sqrt{n/log_2n}}$ steps. To the best of our knowledge, this is the first non-trivial bound for a deterministic SAT algorithm with no restriction on clause length.