Graph Pruning for Enumeration of Minimal Unsatisfiable Subsets

Finding Minimal Unsatisfiable Subsets (MUSes) of boolean constraints is a common problem in infeasibility analysis of over-constrained systems. However, because of the exponential search space of the problem, enumerating MUSes is extremely time-consuming in real applications. In this work, we propose to prune formulas using a learned model to speed up MUS enumeration. We represent formulas as graphs and then develop a graph-based learning model to predict which part of the formula should be pruned. Importantly, the training of our model does not require labeled data. It does not even require training data from the target application because it extrapolates to data with different distributions. In our experiments we combine our model with existing MUS enumerators and validate its effectiveness in multiple benchmarks including a set of real-world problems outside our training distribution. The experiment results show that our method significantly accelerates MUS enumeration on average on these benchmark problems.