SATformer: Transformer-Based UNSAT Core Learning

• URL: http://arxiv.org/abs/2209.00953v2
• Date: Tue, 12 Mar 2024 02:43:40 GMT
• Title: SATformer: Transformer-Based UNSAT Core Learning
• Authors: Zhengyuan Shi (1), Min Li (1), Yi Liu (1), Sadaf Khan (1), Junhua Huang (2), Hui-Ling Zhen (2), Mingxuan Yuan (2), Qiang Xu (1) ((1) The Chinese University of Hong Kong, (2) Huawei Noah's Ark Lab)
• Abstract summary: This paper introduces SATformer, a Transformer-based approach for the Boolean Satisfiability (SAT) problem. Rather than solving the problem directly, SATformer approaches the problem from the opposite direction by focusing on unsatisfiability. SATformer is trained through a multi-task learning approach, using the single-bit satisfiability result and the minimal unsatisfiable core. Experimental results show that our SATformer can decrease the runtime of existing solvers by an average of 21.33%.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces SATformer, a novel Transformer-based approach for the Boolean Satisfiability (SAT) problem. Rather than solving the problem directly, SATformer approaches the problem from the opposite direction by focusing on unsatisfiability. Specifically, it models clause interactions to identify any unsatisfiable sub-problems. Using a graph neural network, we convert clauses into clause embeddings and employ a hierarchical Transformer-based model to understand clause correlation. SATformer is trained through a multi-task learning approach, using the single-bit satisfiability result and the minimal unsatisfiable core (MUC) for UNSAT problems as clause supervision. As an end-to-end learning-based satisfiability classifier, the performance of SATformer surpasses that of NeuroSAT significantly. Furthermore, we integrate the clause predictions made by SATformer into modern heuristic-based SAT solvers and validate our approach with a logic equivalence checking task. Experimental results show that our SATformer can decrease the runtime of existing solvers by an average of 21.33%.

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