Guiding CDCL SAT Search via Random Exploration amid Conflict Depression

Abstract

The efficiency of Conflict Driven Clause Learning (CDCL) SAT solving depends crucially on finding conflicts at a fast rate. State-of-the-art CDCL branching heuristics such as VSIDS, CHB and LRB conform to this goal. We take a closer look at the way in which conflicts are generated over the course of a CDCL SAT search. Our study of the VSIDS branching heuristic shows that conflicts are typically generated in short bursts, followed by what we call a conflict depression phase in which the search fails to generate any conflicts in a span of decisions. The lack of conflict indicates that the variables that are currently ranked highest by the branching heuristic fail to generate conflicts. Based on this analysis, we propose an exploration strategy, called expSAT, which randomly samples variable selection sequences in order to learn an updated heuristic from the generated conflicts. The goal is to escape from conflict depressions expeditiously. The branching heuristic deployed in expSAT combines these updates with the standard VSIDS activity scores. An extensive empirical evaluation with four state-of-the-art CDCL SAT solvers demonstrates good-to-strong performance gains with the expSAT approach.