New Encodings of Pseudo-Boolean Constraints into CNF

Olivier Bailleux (1) , Yacine Boufkhad (2, 3) , Olivier Roussel (4)

1 LIRSIA - Laboratoire Informatique de Recherche sur les Systèmes Intelligents et leurs Applications
2 GANG - Networks, Graphs and Algorithms
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
4 CRIL - Centre de Recherche en Informatique de Lens

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.

Domains: Data Structures and Algorithms [cs.DS]; Computational Complexity [cs.CC]

Olivier Bailleux, Yacine Boufkhad, Olivier Roussel. New Encodings of Pseudo-Boolean Constraints into CNF. Theory and Applications of Satisfiability Testing - SAT 2009, Jun 2009, Swansea, United Kingdom. pp.181-194. ⟨hal-00415126⟩