Réduction et Encodage des Contraintes Ensemblistes en SAT
Frédéric Lardeux, Éric Monfroy · HAL (Le Centre pour la Communication Scientifique Directe) · 2016
On the one hand, Constraint Satisfaction Problems(CSP) are a declarative and expressive approach for mo-deling problems. On the other hand, propositional sa-tisfiability problem (SAT) solvers can handle huge SATinstances up to millions of variables and clauses. In thisarticle, we present an approach for taking advantageof both CSP modeling and SAT solving. Our techniqueconsists in expressively modeling set constraint problemsas CSPs that are automatically treated by some reduc-tion rules to remove values that do not participate inany solution. These reduced CSPs are then encoded into”good” SAT instances that can be solved by standardSAT solvers. We illustrate our technique on various well-known problems such as Sudoku, the Social Golfer pro-blem, and the Sports Tournament Scheduling problem.Our technique is simpler, more expressive, and less error-prone than direct SAT modeling. The SAT instances thatwe automatically generate are rather small (even w.r.t.direct-written SAT instances for the Social Golfer pro-blem [18]) and can efficiently be solved up to huge ins-tances. Moreover, the reduction phase enables to pushback the limits and treat even bigger problems.