A Pseudo-Boolean constraint, PB-constraint, is a linear constraint over Boolean variables. This kind of constraints has been widely used in expressing NP-complete problems. This paper introduces a family of algorithms for translating Pseudo-Boolean constraints into CNF clauses. These algorithms are centered around the idea of rewriting a PB-constraint as the conjunction of a set of easier to translate constraints, we call them PBMod-constraints. The CNF produced by the proposed encoding has small size, and we also characterize the constraints for which one can expect the SAT solvers to perform well on the produced CNF. We show that there are many constraints for which the proposed encoding has a good performance. We compared the running time of SAT solvers on the output of the proposed translation and the existing approaches.

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