Towards Learned Clauses Database Reduction Strategies Based on Dominance Relationship

TL;DR

This paper introduces a novel dominance-based approach for learned clause database reduction in SAT solvers, aiming to select the most relevant clauses without bias towards specific measures and to determine the optimal number of clauses to delete.

Contribution

It proposes a new method leveraging dominance relationships among deletion measures to improve clause relevance assessment and database reduction in SAT solvers.

Findings

The approach effectively balances multiple clause relevance measures.

It avoids bias towards any single clause deletion criterion.

The method determines the optimal number of clauses to delete.

Abstract

Clause Learning is one of the most important components of a conflict driven clause learning (CDCL) SAT solver that is effective on industrial instances. Since the number of learned clauses is proved to be exponential in the worse 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 creates confusion 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 the diversity of results and reaches a compromise between the assessments of these measures. Furthermore, the proposed approach also avoids another non-trivial problem which is the amount of clauses to be deleted at each reduction of the learned clause database.