Solving SAT By Computing A Stable Set Of Points In Clusters

TL;DR

This paper introduces a clustering-based method to compute stable sets of points (SSPs) in CNF formulas, enabling more efficient and parallelizable SAT solving by leveraging formula structure.

Contribution

It proposes a novel clustering approach to compute SSPs for CNF formulas, addressing infeasibility of point-by-point computation and enhancing SAT algorithm efficiency.

Findings

Clustering allows simultaneous processing of large point sets.

SSPs can be computed more efficiently using the proposed method.

The approach facilitates parallel SAT solving.

Abstract

Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that SSPs for CNF formulas of practical interest are very large. So computing an SSP for a CNF formula point by point is, in general, infeasible. In this report, we show how an SSP can be computed in clusters, each cluster being a large set of points that are processed simultaneously. The appeal of computing SSPs is twofold. First, it allows one to better take into account formula structure and hence, arguably, design more efficient SAT algorithms. Second, SAT solving by SSPs facilitates parallel computing.