An Effective Learnt Clause Minimization Approach for CDCL SAT Solvers

Abstract

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).

What a Difference a Variable Makes

“…Satisfiability (SAT) solvers are powerful tools for many applications in formal methods and artificial intelligence [3,9]. Arguably the most effective new techniques in recent years are based on inprocessing [21,25]: Interleaving preprocessing techniques and conflict-driven clause learning (CDCL) [26]. Several powerful inprocessing techniques, such as symmetry breaking [1,6] and blocked clause addition [23], do not preserve logical equivalence and cannot be expressed compactly using classical resolution proofs [30].…”

Clause vivification by unit propagation in CDCL SAT solvers

“…Finally, we show the robustness of our approach by comparing Maple CV+ with several variants and Cadical (version 2018) [43]. Note that Cadical is a non MiniSat-based solver and the used version implements learnt clause vivification in the spirit of the ideas presented in [20].…”

“…Cadical-2017 included inprocessing vivification restricted to irredundant clauses. Cadical-2018 includes, in addition, inprocessing vivification applied to redundant clauses implemented in the spirit of the ideas presented in our IJCAI paper [20]. Here, redundant clauses roughly correspond to the learnt clauses that do not subsume any original clause.…”

“…Moreover, each learnt clause was vivified at most once. This preliminary approach was presented in [20] and implemented in five of the best performing CDCL SAT solvers: Glucose [21], COMiniSatPS [22], MapleCOMSPS [23], MapleCOMSPS LRB [24] and TC Glucose [25]. The experimental results show that the proposed vivification allows these solvers to solve a remarkable number of additional instances coming from the hard combinatorial and application categories of the SAT Competition 2014 and 2016.…”

Tuning Parallel SAT Solvers

“…On the next restart, search is interrupted and the solver thread tries to minimize each of the stored clauses before sending them. A similar idea is presented in [38] in order to strengthen clauses in the learnt clause database of a sequential solver. The rationale behind this approach is that after learning the clause, the solver has backtracked and continued its search in a similar part of the search space.…”