#3250. SAT encodings for Pseudo-Boolean constraints together with at-most-one constraints

July 2026publication date
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Arts and Humanities (miscellaneous);
Developmental and Educational Psychology;
Experimental and Cognitive Psychology;
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Abstract:
When solving a combinatorial problem using propositional satisfiability, the encoding of the problem is of vital importance. We study encodings of Pseudo-Boolean (PB) constraints, a common type of arithmetic constraint that appears in a wide variety of combinatorial problems such as timetabling, scheduling, and resource allocation. The research presents a more compact and efficient version of the popular Generalized Totalizer encoding, named Reduced Generalized Totalizer. This new encoding is also adapted for constraints for a further gain. Our experiments show that the encodings of constraints can be substantially smaller than those of constraints. 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.
Keywords:
At-most-one constraints; Encoding; Pseudo-Boolean constraints

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