Linear Programming Formulation of the Boolean Satisfiability Problem

TL;DR

This paper introduces a novel graph-based linear programming formulation for the Boolean satisfiability problem, providing a polynomial-sized model that offers a new perspective on solving SAT efficiently.

Contribution

It presents the first polynomial-sized LP formulation of SAT using a graph-based approach, advancing the modeling techniques for this fundamental problem.

Findings

LP formulation is polynomial in size

Graph-based approach effectively models SAT constraints

Numerical example demonstrates practical applicability

Abstract

In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.