Translating Pseudo-Boolean Constraints into SAT

Niklas Een, Niklas Sorensson


In this paper, we describe and evaluate three different techniques for translating pseudo-boolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SAT-solver. We show that by applying a proper mix of translation techniques, a SAT-solver can perform on a par with the best existing native pseudo-boolean solvers. This is particularly valuable in those cases where the constraint problem of interest is naturally expressed as a SAT problem, except for a handful of constraints. Translating those constraints to get a pure clausal problem will makke full advantage of the latest improvements in SAT research. A particularly interesting result of this work is the efficiency of sorting networks to express pseudo-boolean constraints. Although tangential to this presentation, the result gives a suggestion as to how synthesis tools may be modified to produce arithmetic circuits more suitable for SAT based reasoning.


pseudo-Boolean, SAT-solver, SAT translation, integer linear programming

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