From Set Constraint Models to SAT Instances

Abstract

On the one hand, Constraint Satisfaction Problems (CSP) are a declarative and expressive approach for modeling problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances up to millions of variables and clauses. In this article, we present an approach for taking advantage of both CSP modeling and SAT solving. Our technique consists in expressively modeling set constraint problems as CSPs that are automatically treated by some reduction rules to remove values that do not participate in any solution. These reduced CSPs are then encoded into good SAT instances that can be solved by standard SAT solvers. We illustrate our technique on the Sports Tournament Scheduling problem, and we show that we obtain competitive results compared to an ad-hoc solver. Our technique is simpler, more expressive, and less error-prone than direct SAT modeling. The SAT instances that we automatically generate are rather small and can efficiently be solved up to huge instances. Moreover, the reduction phase enables to push back the limits and treat even larger problems.