New Encodings of Pseudo-Boolean Constraints into CNF

Authors:
Olivier Bailleux;Yacine Boufkhad;Olivier Roussel
Affiliations:
LERSIA --- Université de Bourgogne,;LIAFA, CNRS, Gang team INRIA, Université Paris Diderot, France;Université Lille-Nord de France, Artois, F-62307 Lens --- CRIL, F-62307, Lens --- CNRS UMR 8188, Lens, F-62307
Venue:
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Year:
2009

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Abstract

This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.