SAT with Global Constraints

Abstract

Propositional satisability (SAT) has been a dominant tool in solving some practical NP-complete problems. However, SAT also has a number of weaknesses, including its inability to compactly represent numerical constraints and its low level, unstructured language of clauses. In contrast, Constraint Programming (CP) has been widely used for scheduling and solving combinatorial search problems. In this thesis, we develop a tight integration of SAT with CP, called SAT(gc), which embeds global constraints, one of the most efficient features of CP, into SAT. We devise a DPLL-based algorithm for a SAT(gc) solver. A prototype system is implemented by integrating the state of the art SAT solver Zchaff and the generic constraint solver named Gecode. Experiments are carried out for benchmarks from puzzle domains and planning domains to reveal insights in compact representation, solving effectiveness, and novel usabilities of the new framework.