Revisiting the Learned Clauses Database Reduction Strategies

Abstract

In this paper, we revisit an important issue of CDCL-based SAT solvers, namely the learned clauses database management policies. Our motivation takes its source from a simple observation on the remarkable performances of both random and size-bounded reduction strategies. We first derive a simple reduction strategy, called Size-Bounded Randomized strategy (in short SBR), that combines maintaining short clauses (of size bounded by k), while deleting randomly clauses of size greater than k. The resulting strategy outperform the state-of-the-art on SAT instances taken from the SAT competitions 2013 and 2018, and remains competitive on a broad range of SAT instances of the SAT Competition 2014. Reinforced by the interest of keeping short clauses, we propose several new dynamic variants, and we discuss their performance. We also propose different ways for adjusting dynamically the size-bounded parameter of the strategy.

Towards Learned Clauses Database Reduction Strategies Based on Dominance Relationship

“…In [2], the authors consider the clause c 1 which has the most smallest LBD measure as the most relevant. In contrast, the authors of [15] and [12] prefer the clause c 3 while the preference of the authors of Minisat [11] leads to the clause c 3 . Our approach copes with the particular preference at one measure by finding a compromise between the different relevant measures through the dominance relationship.…”

“…Starting from this observation, and motivated by the fact that a learned clause with smaller BTL contains more literals from the top of the search tree, the authors deduce that relevant clauses are those allowing a higher backtracking in the search tree (having small BTL value). More recently, several other learned clauses database strategies were proposed in [15,1]. In [15], the authors explore a number of variations of learned clause database reduction strategies, and the performance of the different extensions of Minisat solver integrating their strategies is evaluated on the instances of the SAT competitions 2013/2014 and compared against other state-of-the-art SAT solvers (Glucose, Lingeling) as well as against default Minisat.…”

“…More recently, several other learned clauses database strategies were proposed in [15,1]. In [15], the authors explore a number of variations of learned clause database reduction strategies, and the performance of the different extensions of Minisat solver integrating their strategies is evaluated on the instances of the SAT competitions 2013/2014 and compared against other state-of-the-art SAT solvers (Glucose, Lingeling) as well as against default Minisat. From the performances obtained in [15], the authors have shown that size-bounded learning strategies proposed more than fifteenth years ago [19,4,5] is not over and remains a good measure to predict the quality of learned clauses.…”

“…In [15], the authors explore a number of variations of learned clause database reduction strategies, and the performance of the different extensions of Minisat solver integrating their strategies is evaluated on the instances of the SAT competitions 2013/2014 and compared against other state-of-the-art SAT solvers (Glucose, Lingeling) as well as against default Minisat. From the performances obtained in [15], the authors have shown that size-bounded learning strategies proposed more than fifteenth years ago [19,4,5] is not over and remains a good measure to predict the quality of learned clauses. They show that adding randomization to size bounded learning is a nice way to achieve controlled diversification, allows to favor the short clauses, while maintaining a small fraction of large clauses necessary for deriving resolution proofs on some SAT instances.…”

SAT and CP - Parallelisation and Applications

“…On the other hand, keeping a lot of learned clauses slows down the propagation process, and may even cause the solver to run out of memory. Therefore, solvers clean their learned clause database regularly and delete some of the learned clauses [19,111,126,169].…”