0000000000290727
AUTHOR
Olivier Roussel
A Translation of Pseudo Boolean Constraints to SAT
Research note; This paper introduces a new CNF encoding of pseudo-Boolean constraints, which allows unit propagation to maintain generalized arc consistency. In the worst case, the size of the produced formula can be exponentially related to the size of the input constraint, but some important classes of pseudo-Boolean constraints, including Boolean cardinality constraints, are encoded in polynomial time and size. The proposed encoding was integrated in a solver based on the zCha SAT solver and submitted to the PB05 evaluation. The results provide new perspectives in the field of full CNF approach of pseudo-Boolean constraints solving.
New Encodings of Pseudo-Boolean Constraints into CNF
International audience; 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.