Generalizing Boolean Satisfiability II: Theory

TL;DR

This paper develops the theoretical foundation for ZAP, a generalized SAT solver that leverages problem structure through group theory to enhance computational efficiency, extending existing inference methods.

Contribution

It introduces a theoretical framework based on group structures to generalize SAT solving, extending the Davis-Putnam-Logemann-Loveland procedure.

Findings

Theoretical basis for exploiting problem structure in SAT solving

Extension of inference procedures to broader structural settings

Preservation of computational improvements in the generalized approach

Abstract

This is the second 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 presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results.