A Hybrid Encoding of Pseudo-Boolean Constraints into CNF

Abstract

Many NP-hard problems are commonly expressed with pseudo-Boolean (PB) constraints, which is a linear arithmetic constraint over Boolean variables. Conjunctive Normal Form (CNF) encoding always plays an important role in solving these constraints. In this paper, we propose Weighted Modulo Totalizer (WMTO) which is a hybrid CNF encoding of PB constraints between Modulo Totalizer (MTO) and Weighted Totalizer (WTO). WMTO uses less clauses and auxiliary variables than each of them. Our experimental results show that WMTO encodes the constraints compactly and the obtained clauses are efficiently handled by a state-of-the-art SAT solver