Top-k Learned Clauses for Modern SAT Solvers

Abstract

Clause Learning is one of the most important components of a conflict driven clause learning (CDCL) SAT solver that is effective on industrial SAT instances. Since the number of learned clauses is proved to be exponential in the worst case, it is necessary to identify the most relevant clauses to maintain and delete the irrelevant ones. As reported in the literature, several learned clauses deletion strategies have been proposed. However the diversity in both the number of clauses to be removed at each step of reduction and the results obtained with each strategy increase the difficulty to determine which criterion is better. Thus, the problem to select which learned clauses are to be removed during the search step remains very challenging. In this paper, we propose a novel approach to identify the most relevant learned clauses without favoring or excluding any of the proposed measures, but by adopting the notion of dominance relationship among those measures. Our approach bypasses the problem of difference in the results obtained with different measures and reaches a compromise between the measures assessments. Furthermore, the proposed approach also reduces the non-trivial problem of choosing the number of clauses to delete at each reduction of the learned clause database.