Clause Vivification by Unit Propagation in CDCL SAT Solvers

TL;DR

This paper introduces a clause vivification method using unit propagation to remove redundant literals in CDCL SAT solvers, improving their performance on hard instances.

Contribution

It proposes a novel clause vivification technique activated before restarts, selectively applied to relevant clauses, and demonstrates its effectiveness through extensive empirical evaluation.

Findings

Increases the number of solved instances in SAT competitions.

Improves solver performance on hard combinatorial and application instances.

Contributes to a solver that ranked first in SAT Competition 2017 and won bronze in 2018.

Abstract

Original and learnt clauses in Conflict-Driven Clause Learning (CDCL) SAT solvers often contain redundant literals. This may have a negative impact on performance because redundant literals may deteriorate both the effectiveness of Boolean constraint propagation and the quality of subsequent learnt clauses. To overcome this drawback, we propose a clause vivification approach that eliminates redundant literals by applying unit propagation. The proposed clause vivification is activated before the SAT solver triggers some selected restarts, and only affects a subset of original and learnt clauses, which are considered to be more relevant according to metrics like the literal block distance (LBD). Moreover, we conducted an empirical investigation with instances coming from the hard combinatorial and application categories of recent SAT competitions. The results show that a remarkable number of additional instances are solved when the proposed approach is incorporated into five of the best performing CDCL SAT solvers (Glucose, TC_Glucose, COMiniSatPS, MapleCOMSPS and MapleCOMSPS_LRB). More importantly, the empirical investigation includes an in-depth analysis of the effectiveness of clause vivification. It is worth mentioning that one of the SAT solvers described here was ranked first in the main track of SAT Competition 2017 thanks to the incorporation of the proposed clause vivification. That solver was further improved in this paper and won the bronze medal in the main track of SAT Competition 2018.