Generalizing Boolean Satisfiability I: Background and Survey of Existing Work

TL;DR

This paper surveys prior work on enhancing Boolean satisfiability solvers by exploiting problem structure, laying the groundwork for the ZAP engine that generalizes existing tools while maintaining high performance.

Contribution

It provides a comprehensive survey of structural techniques in SAT solving, setting the stage for the development of the ZAP engine that extends these ideas.

Findings

Survey of structural enhancements in SAT solvers

Discussion of extensions like cardinality constraints and symmetry

Foundation for the ZAP satisfiability engine

Abstract

This is the first of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper is a survey of the work underlying ZAP, and discusses previous attempts to improve the performance of the Davis-Putnam-Logemann-Loveland algorithm by exploiting the structure of the problem being solved. We examine existing ideas including extensions of the Boolean language to allow cardinality constraints, pseudo-Boolean representations, symmetry, and a limited form of quantification. While this paper is intended as a survey, our research results are contained in the two subsequent articles, with the theoretical structure of ZAP described in the second paper in this series, and ZAP's implementation described in the third.