A Deep Dive into Conflict Generating Decisions

Boolean Satisfiability (SAT) is a well-known NP-complete problem. Despite this theoretical hardness, SAT solvers based on Conflict Driven Clause Learning (CDCL) can solve large SAT instances from many important domains. CDCL learns clauses from conflicts, a technique that allows a solver to prune its search space. The selection heuristics in CDCL prioritize variables that are involved in recent conflicts. While only a fraction of decisions generate any conflicts, many generate multiple conflicts. In this paper, we study conflict-generating decisions in CDCL in detail. We investigate the impact of single conflict (sc) decisions, which generate only one conflict, and multi-conflict (mc) decisions which generate two or more. We empirically characterize these two types of decisions based on the quality of the learned clauses produced by each type of decision. We also show an important connection between consecutive clauses learned within the same mc decision, where one learned clause triggers the learning of the next one forming a chain of clauses. This leads to the consideration of similarity between conflicts, for which we formulate the notion of conflictsproximity as a similarity measure. We show that conflicts in mc decisions are more closely related than consecutive conflicts generated from sc decisions. Finally, we develop Common Reason Variable Reduction (CRVR) as a new decision strategy that reduces the selection priority of some variables from the learned clauses of mc decisions. Our empirical evaluation of CRVR implemented in three leading solvers demonstrates performance gains in benchmarks from the main track of SAT Competition-2020.