Should Algorithms for Random SAT and Max-SAT be Different?

TL;DR

This paper investigates the differences between algorithms for random SAT and Max-SAT, proposing a new probabilistic solver for Max-SAT that outperforms existing methods on benchmarks.

Contribution

It analyzes the properties of random SAT and Max-SAT, and introduces ProMS, a novel probabilistic approach specifically designed for random Max-SAT.

Findings

Max-SAT can be solved by SAT algorithms with subexponential slowdown in certain regimes.

Different heuristics are needed for high-ratio formulas under the random walk framework.

ProMS outperforms state-of-the-art local search solvers on random Max-SAT benchmarks.

Abstract

We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random $k$-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown, while for formulae with ratios greater than some constant, algorithms under the random walk framework require substantially different heuristics. In light of these results, we propose a novel probabilistic approach for random Max-SAT called ProMS. Experimental results illustrate that ProMS outperforms many state-of-the-art local search solvers on random Max-SAT benchmarks.