The Boolean Satisfiability (SAT) problem stands out as an attractive NP-complete problem in theoretic computer science and plays a central role in a broad spectrum of computing-related applications. Exploiting and tuning SAT solvers under numerous scenarios require massive high-quality industry-level SAT instances, which unfortunately are quite limited in the real world. To address the data insufficiency issue, in this paper, we propose W2SAT, a framework to generate SAT formulas by learning intrinsic structures and properties from given real-world/industrial instances in an implicit fashion. To this end, we introduce a novel SAT representation called Weighted Literal Incidence Graph (WLIG), which exhibits strong representation ability and generalizability against existing counterparts, and can be efficiently generated via a specialized learning-based graph generative model. Decoding from WLIGs into SAT problems is then modeled as finding overlapping cliques with a novel hill-climbing optimization method termed Optimal Weight Coverage (OWC). Experiments demonstrate the superiority of our WLIG-induced approach in terms of graph metrics, efficiency, and scalability in comparison to previous methods. Additionally, we discuss the limitations of graph-based SAT generation for real-world applications, especially when utilizing generated instances for SAT solver parameter-tuning, and pose some potential directions.

本文提出了一种基于WLIG的SAT公式生成框架W2SAT，并通过实验证明了WLIG的优越性及其与其他方法的差异，并讨论了其在实际应用中的局限性以及可能的解决方案。

W2SAT: 从加权文字关系图中学习生成SAT实例