Predicting Propositional Satisfiability Based on Graph Attention Networks

Abstract

Boolean satisfiability problems (SAT) have very rich generic and domain-specific structures. How to capture these structural features in the embedding space and feed them to deep learning models is an important factor influencing the use of neural networks to solve SAT problems. Graph neural networks have achieved good results, especially for message-passing models. These capture the displacement-invariant architecture well, whether building end-to-end models or improving heuristic algorithms for traditional solvers. We present the first framework for predicting the satisfiability of domain-specific SAT problems using graph attention networks, GAT-SAT. Our model can learn satisfiability features in a weakly supervised setting, i.e., in the absence of problem-specific feature engineering. We test the model to predict the satisfiability of randomly generated SAT instances SR(N) and random 3-SAT problems. Experiments demonstrate that our model improves the prediction accuracy of random 3-SAT problems by 1–4% and significantly outperforms other graph neural network approaches on random SR(N). Compared to NeuroSAT, our model can almost always achieve the same or even higher accuracy with half the amount of iterations. At the end of the paper, we also try to explain the role played by the graph attention mechanism in the model.