The Elephant in the Room: Variable Dependency in GNN-based SAT Solving

Zhiyuan Yan, Min Li, Zhengyuan Shi, Wenjie Zhang, Ying-Cong Chen, Hongce Zhang

Keywords: SAT Solving, Graph Neural Networks, Variable Dependency

TL;DR: We address the variable dependency problem in SAT solving by a new GNN-based model.

Abstract: Boolean satisfiability problem (SAT) is fundamental to many applications. Existing works have used graph neural networks (GNNs) for (approximate) SAT solving. Typical GNN-based end-to-end SAT solvers predict SAT solutions concurrently. We show that for a group of symmetric SAT problems, the concurrent prediction is guaranteed to produce a wrong answer because it neglects the dependency among Boolean variables in SAT problems. We propose AsymSAT, a GNN-based architecture which integrates recurrent neural networks to generate dependent predictions for variable assignments. The experiment results show that dependent variable prediction extends the solving capability of the GNN-based method as it improves the number of solved SAT instances on large test sets.