Boosting the Performance of CDCL-Based SAT Solvers by Exploiting Backbones and Backdoors

Abstract

Boolean structural measures were introduced to explain the high performance of conflict-driven clause-learning (CDCL) SAT solvers on industrial SAT instances. Those considered in this study include measures related to backbones and backdoors: backbone size, backbone frequency, and backdoor size. A key area of research is to improve the performance of CDCL SAT solvers by exploiting these measures. For the purpose of guiding the CDCL SAT solver for branching on backbone and backdoor variables, this study proposes low-overhead heuristics for computing these variables. Through these heuristics, a set of modifications to the Variable State Independent Decaying Sum (VSIDS) decision heuristic is suggested to exploit backbones and backdoors and potentially improve the performance of CDCL SAT solvers. In total, fifteen variants of two competitive base solvers, MapleLCMDistChronoBT-DL-v3 and LSTech, were developed. Empirical evaluation was conducted on 32 industrial families from 2002–2021 SAT competitions. According to the results, modifying the VSIDS heuristic in the base solvers to exploit backbones and backdoors improves its performance. In particular, our new CDCL SAT solver, LSTech_BBsfcr_v1, solved more industrial SAT instances than the winning CDCL SAT solvers in 2020 and 2021 SAT competitions.