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This paper introduces a novel graph neural network (GNN) architecture for unsat-core prediction in SAT formulas, modeling formulas as clause-literal hypergraphs augmented with clause incidence graphs. The key innovation is a polarity-aware decomposed mechanism that separates variable representations into polarity invariant and equivariant components, explicitly capturing the relationship between positive and negative literals. Experiments on multiple SAT datasets demonstrate that this approach outperforms existing GNN-based methods for unsat-core prediction.
By explicitly modeling literal polarity in SAT formulas, GNNs can more accurately predict unsatisfiable cores.
Graph neural networks have been widely used in Boolean satisfiability (SAT) tasks to learn structural information from SAT formulas. The goal of these studies is to solve SAT instances or to enhance SAT solvers, including tasks such as unsat-core prediction. However, most existing approaches model a SAT formula as a bipartite graph or a directed acyclic graph, which are less expressive in capturing higher-order interactions among literals and clauses. Moreover, these approaches are limited in modeling intrinsic polarity-related properties of SAT, such as the complementary relationship between the positive and negative literals of a variable. To address these limitations, we propose a polarity-aware representation learning framework over clause-literal hypergraphs. We model SAT formulas as clause-literal hypergraphs augmented with a clause incidence graph to capture higher-order structural interactions. We then introduce a polarity-aware decomposed mechanism that separates variable representations into polarity invariant and equivariant components, explicitly modeling the relationship between positive and negative literals, with the resulting literal representations propagated along the hypergraph structure. We further incorporate a polarity-inversion consistency regularization to reinforce polarity-consistent representations during training. Experimental results on multiple SAT datasets demonstrate the effectiveness of the proposed approach.
