Solving Pseudo-Boolean Modularity Constraints

This paper introduces new solving strategies for the resolution of Pseudo-Boolean Modularity (PBMod) constraints. In particular, we deal with modular arithmetic constraints on Boolean variables. On the one hand, we analyze translations to Pseudo-Boolean (PB) constraints and apply PB solvers. We also look at those PB solvers that have shown that a transformation to the SAT problem can be an effective solving strategy for PB problems. Among the existing translation techniques we focus on the encoding based on a network of sorters. We extend this encoding technique to generate directly a SAT formula from the PBMod constraints. We compare our approach to other standard techniques such as Satisfiability Modulo Theories (SMT) solvers with support for the Quantifier Free Linear Integer Arithmetic (QF_LIA) theory and the GLPK package for Mixed Integer Programming. In order to conduct our experimental investigation we present a generator of random PBMod constraints and study the impact of the several parameters on the hardness of the instances.

Authors

• Carlos Ansótegui
• Ramón Béjar
• Cèsar Fernández 0001
• Francesc Guitart
• Carles Mateu

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