Advancing Stochastic 3-SAT Solvers by Dissipating Oversatisfied Constraints

TL;DR

This paper presents DOCSAT, a novel stochastic local search heuristic for 3-SAT that outperforms existing solvers by dissipating oversatisfied constraints, effectively escaping local minima in hard instances.

Contribution

Introduces DOCSAT, a new algorithm that reduces oversatisfied constraints to improve performance on hard 3-SAT problems, surpassing existing solvers.

Findings

DOCSAT outperforms WalkSAT and Kissat on hard 3-SAT instances.

DOCSAT effectively solves larger problem sizes up to N=15000.

Dissipating oversatisfied constraints helps escape local minima in stochastic search.

Abstract

We introduce and benchmark a stochastic local search heuristic for the NP-complete satisfiability problem 3-SAT that drastically outperforms existing solvers in the notoriously difficult realm of critically hard instances. Our construction is based on the crucial observation that well established previous approaches such as WalkSAT are prone to get stuck in local minima that are distinguished from true solutions by a larger number of oversatisfied combinatorial constraints. To address this issue, the proposed algorithm, coined DOCSAT, dissipates oversatisfied constraints (DOC), i.e. reduces their unfavorable abundance so as to render them critical. We analyze and benchmark our algorithm on a randomly generated sample of hard but satisfiable 3-SAT instances with varying problem sizes up to N=15000. Quite remarkably, we find that DOCSAT outperforms both WalkSAT and other well known algorithms including the complete solver Kissat, even when comparing its ability to solve the hardest quintile of the sample to the average performance of its competitors. The essence of DOCSAT may be seen as a way of harnessing statistical structure beyond the primary cost function of a combinatorial problem to avoid or escape local minima traps in stochastic local search, which opens avenues for generalization to other optimization problems.