Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints

Abstract

Pseudo-Boolean (PB) constraints often have a critical role in constraint satisfaction and optimisation problems. Encoding PB constraints to SAT has proven to be an efficient approach in many applications, however care must be taken to encode them compactly and with good propagation properties. It has been shown that at-most-one (AMO) and exactly-one (EO) relations over subsets of the variables can be exploited in various encodings of PB constraints, improving their compactness and solving performance. In this paper we detect AMO and EO relations completely automatically and exploit them to improve SAT encodings that are based on Multi-Valued Decision Diagrams (MDDs). Our experiments show substantial reductions in encoding size and dramatic improvements in solving time thanks to automatic AMO and EO detection.