A Linear Weight Transfer Rule for Local Search

The Divide and Distribute Fixed Weights algorithm (ddfw) is a dynamic local search SAT-solving algorithm that transfers weight from satisfied to falsified clauses in local minima. ddfw is remarkably effective on several hard combinatorial instances. Yet, despite its success, it has received little study since its debut in 2005. In this paper, we propose three modifications to the base algorithm: a linear weight transfer method that moves a dynamic amount of weight between clauses in local minima, an adjustment to how satisfied clauses are chosen in local minima to give weight, and a weighted-random method of selecting variables to flip. We implemented our modifications to ddfw on top of the solver yalsat. Our experiments show that our modifications boost the performance compared to the original ddfw algorithm on multiple benchmarks, including those from the past three years of SAT competitions. Moreover, our improved solver exclusively solves hard combinatorial instances that refute a conjecture on the lower bound of two Van der Waerden numbers set forth by Ahmed et al. (2014), and it performs well on a hard graph-coloring instance that has been open for over three decades

Guiding CDCL SAT Search via Random Exploration amid Conflict Depression

The efficiency of Conflict Driven Clause Learning (CDCL) SAT solving depends crucially on finding conflicts at a fast rate. State-of-the-art CDCL branching heuristics such as VSIDS, CHB and LRB conform to this goal. We take a closer look at the way in which conflicts are generated over the course of a CDCL SAT search. Our study of the VSIDS branching heuristic shows that conflicts are typically generated in short bursts, followed by what we call a conflict depression phase in which the search fails to generate any conflicts in a span of decisions. The lack of conflict indicates that the variables that are currently ranked highest by the branching heuristic fail to generate conflicts. Based on this analysis, we propose an exploration strategy, called expSAT, which randomly samples variable selection sequences in order to learn an updated heuristic from the generated conflicts. The goal is to escape from conflict depressions expeditiously. The branching heuristic deployed in expSAT combines these updates with the standard VSIDS activity scores. An extensive empirical evaluation with four state-of-the-art CDCL SAT solvers demonstrates good-to-strong performance gains with the expSAT approach

Exploring Conflict Generating Decisions: Initial Results (Extended Abstract)

Boolean Satisfiability (SAT) is an NP-complete problem, indicating its inherent computational hardness. However, Conflict Driven Clause Learning (CDCL) SAT solvers efficiently tackle large instances in diverse domains. Swift conflict identification is crucial for effective problem-solving, as conflicts lead to the learning of search space pruning clauses, pinpointing the root causes of conflicts and preventing their recurrence. CDCL decision heuristics prioritize variables that participated in recent conflicts, anticipating rapid conflict generation and expediting additional clause learning. In practice, only a fraction of decisions lead to conflicts, yet some decisions may yield multiple conflicts. In this paper, we delve into a detailed study of conflict generating decisions in CDCL, distinguishing between single conflict (sc) decisions, generating only one conflict, and multi-conflict (mc) decisions, producing two or more conflicts. Our empirical analysis characterizes each decision type based on the quality of the learned clauses they produce. Furthermore, our theoretical analysis reveals a crucial distinction: consecutive clauses learned within the same mc decision form a chain of clauses, absent in learned clauses from sc decisions. This leads to the hypothesis that the reasons for conflicts in mc decisions are more closely related than the reasons for conflicts in sc decisions, empirically confirmed with our introduced notion of reason proximity. Finally, we propose score reduction (sr) as a novel decision strategy, reducing the selection priority of certain variables from learned clauses in mc decisions. With four sets of benchmarks, culminating in over 1200 benchmarks, empirical evaluation of sr implemented on top of the SAT competition 2023 winner solver reveals the merit of this new strategy

Preliminary Results on Exploration-Driven Satisfiability Solving

In this abstract, we present our study of exploring the SAT search space via random-sampling, with the goal of improving Conflict Directed Clause Learning (CDCL) SAT solvers. Our proposed CDCL SAT solving algorithm expSAT uses a novel branching heuristic expVSIDS. It combines the standard VSIDS scores with heuristic scores derived from exploration. Experiments with application benchmarks from recent SAT competitions demonstrate the potential of the expSAT approach for improving CDCL SAT solvers

Migrating Solver State

We present approaches to store and restore the state of a SAT solver, allowing us to migrate the state between different compute resources, or even between different solvers. This can be used in many ways, e.g., to improve the fault tolerance of solvers, to schedule SAT problems on a restricted number of cores, or to use dedicated preprocessing tools for inprocessing. We identify a minimum viable subset of the solver state to migrate such that the loss of performance is small. We then present and implement two different approaches to state migration: one approach stores the state at the end of a solver run whereas the other approach stores the state continuously as part of the proof trace. We show that our approaches enable the generation of correct models and valid unsatisfiability proofs. Experimental results confirm that the overhead is reasonable and that in several cases solver performance actually improves