Abstract
In this paper, we present a Bayesian Moment Matching (BMM) in-processing technique for Conflict-Driven Clause-Learning (CDCL) SAT solvers. BMM is a probabilistic algorithm which takes as input a Boolean formula in conjunctive normal form and a prior on a possible satisfying assignment, and outputs a posterior for a new assignment most likely to maximize the number of satisfied clauses. We invoke this BMM method, as an in-processing technique, with the goal of updating the polarity and branching activity scores. The key insight underpinning our method is that Bayesian reasoning is a powerful way to guide the CDCL search procedure away from fruitless parts of the search space of a satisfiable Boolean formula, and towards those regions that are likely to contain satisfying assignments.
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Notes
- 1.
The
function implements the Boolean constraint propagation (BCP) procedure that forces (in cascade) the values of variables in unit clauses [6]. - 2.
These magic numbers are borrowed from the base solver that we used for our implementation.
- 3.
- 4.
function implements the Boolean constraint propagation (BCP) procedure that forces (in cascade) the values of variables in unit clauses [References
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Vallade, V., Nejati, S., Sopena, J., Baarir, S., Ganesh, V. (2022). Diversifying a Parallel SAT Solver with Bayesian Moment Matching. In: Dong, W., Talpin, JP. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2022. Lecture Notes in Computer Science, vol 13649. Springer, Cham. https://doi.org/10.1007/978-3-031-21213-0_14
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