Improved Binary Decision Diagram Constraint Propagation for Satisfiability Problems

Abstract

In general, search-based solvers have been dominating symbolic solvers according to experimental results reported in the SAT and QBF literature. However, some recent efforts have contributed to close that performance gap. One novel approach involves the use of Binary Decision Diagrams(BDDs) and a simplification routine called BDD constraint propagation. The main idea is to adapt optimizations from search-based solvers in the context of BDDs. In this paper we improve upon the existing BDD constraint propagation procedure. Concretely, for a BDD A and its support set SupportSet(A), we reduce the asymptotic upper bound for the clause BDD pure literal extraction from O(A * SupportSet(A)) to O(n) time and nonclause BDD unit literal extraction from O(A * SupportSet(A)) to O(A) time. We also formulate for the first time the Trivial Falsity, Forced Literal and Universal Reduction rules for BDDs. We show in the experimental section that these improvements allow a BDD-based solver to tackle new families of problems, and outperform state-of-the art solvers in some cases.