From Clauses to Klauses

Abstract Satisfiability (SAT) solvers have been using the same input format for decades: a formula in conjunctive normal form. Cardinality constraints appear frequently in problem descriptions: over $64\%$ 64 % of the SAT Competition formulas contain at least one cardinality constraint, while over $17\%$ 17 % contain many large cardinality constraints. Allowing general cardinality constraints as input would simplify encodings and enable the solver to handle constraints natively or to encode them using different (and possibly dynamically changing) clausal forms. We modify the modern SAT solver CaDiCaL to handle cardinality constraints natively. Unlike the stronger cardinality reasoning in pseudo-Boolean (PB) or other systems, our incremental approach with cardinality-based propagation requires only moderate changes to a SAT solver, preserves the ability to run important inprocessing techniques, and is easily combined with existing proof-producing and validation tools. Our experimental evaluation on SAT Competition formulas shows our solver configurations with cardinality support consistently outperform other SAT and PB solvers.