Learnt clauses in 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 define a new inprocessing SAT approach which eliminates redundant literals from learnt clauses by applying Boolean constraint propagation. Learnt clause minimization is activated before the SAT solver triggers some selected restarts, and affects only some learnt clauses during the search process. Moreover, we conducted an empirical evaluation on 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 approach is incorporated into five of the best performing CDCL SAT solvers (Glucose, TC Glucose, COMiniSatPS, MapleCOMSPS and MapleCOMSPS LRB).
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.
Bounded Variable Elimination (BVE) is an important Boolean formula simplification technique in which the variable ordering is crucial. We define a new variable ordering based on variable activity, called ESA (variable Elimination Scheduled by Activity), for in-processing BVE in Conflict-Driven Clause Learning (CDCL) SAT solvers, and incorporate it into several state-of-the-art CDCL SAT solvers. Experimental results show that the new ESA ordering consistently makes these solvers solve more instances on the benchmark set including all the 5675 instances used in the Crafted, Application and Main tracks of all SAT Competitions up to 2022. In particular, one of these solvers with ESA, Kissat_MAB_ESA, won the Anniversary track of the SAT Competition 2022. The behaviour of ESA and the reason of its effectiveness are also analyzed.
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