Approximately Propagation Complete and Conflict Propagating Constraint Encodings
The effective use of satisfiability (SAT) solvers requires problem encodings that make good use of the reasoning techniques employed in such solvers, such as unit propagation and clause learning. Propagation completeness has been proposed as a useful property for constraint encodings as it maximizes the utility of unit propagation. Experimental results on using encodings with this property in the context of satisfiability modulo theory (SMT) solving have however remained inconclusive, as such encodings are typically very large, which increases the bookkeeping work of solvers.
In this paper, we introduce approximate propagation completeness and approximate conflict propagation as novel SAT encoding property notions. While approximate propagation completeness is a generalization of classical propagation completeness, (approximate) conflict propagation is a new concept for reasoning about how early conflicts can be detected by a SAT solver. Both notions together span a hierarchy of encoding quality choices, with classical propagation completeness as a special case. We show how to compute approximately propagation complete and conflict propagating constraint encodings with a minimal number of clauses using a reduction to MaxSAT. To evaluate the effect of such encodings, we give results on applying them in a case study.
This work was supported by DFG grant EH 481/1-1 and the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative. The authors want to thank Armin Biere for early feedback on the propagation quality notions defined in this work and Erika Abraham for proposing MaxSAT solvers as reasoning backend.
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