#3726. SAT encodings for Pseudo-Boolean constraints together with at-most-one constraints

October 2026publication date
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Artificial Intelligence;
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Abstract:
When solving a combinatorial problem using propositional satisfiability (SAT), the encoding of the problem is of vital importance. Recent work has shown that taking account of AMOs when encoding PB constraints using decision diagrams can produce a dramatic improvement in solver efficiency. This new encoding is also adapted for PB(AMO) constraints for a further gain. Our experiments show that the encodings of PB(AMO) constraints can be substantially smaller than those of PB constraints. PB(AMO) encodings allow many more instances to be solved within a time limit, and solving time is improved by more than one order of magnitude in some cases. We also observed that there is no single overall winner among the considered encodings.
Keywords:
At-most-one constraints; Encoding; Pseudo-Boolean constraints

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