DiffSAT: Differential MaxSAT Layer for SAT Solving

Modern boolean satisfiability (SAT) solvers heavily rely on the conflict-driven clause learning (CDCL) framework to efficiently search the solution space and resolve conflicts during the search process. However, CDCL still faces challenges in terms of searching efficiency, particularly in complex cases with deep/symmetric/tree-based structures. To address this issue, numerous learning-driven methods have been proposed. However, these methods primarily focus on utilizing data-driven approaches to enhance searching efficiency and decision accuracy, while overlooking the core issue of the state explosion within the CDCL framework itself when the search starts at the wrong point. In this paper, we introduce DiffSAT, a novel approach that differentiates the discrete SAT problem and progressively searches for satisfying assignments through the forward and backward propagation of a neural network layer. DiffSAT initiates with an initial assignment obtained through semidefinite approximation and iteratively explores the solution space guided by a differential loss function. Notably, DiffSAT does not require training data and can be applied to large-scale problems that have not been seen before. The experimental results provide evidence that DiffSAT exhibits superior performance compared to existing end-to-end learning-based SAT solvers and can be generalized to solve large-scale SAT problems. Additionally, DiffSAT surpasses state-of-the-art SAT solvers in effectively finding satisfying assignments for complex problems in SATCOMP-2023.