SAT-GATv2: A Dynamic Attention-Based Graph Neural Network for Solving Boolean Satisfiability Problem
We propose SAT-GATv2, a graph neural network (GNN)-based model designed to solve the Boolean satisfiability problem (SAT) through graph-based deep learning techniques. SAT-GATv2 transforms SAT formulas into graph structures, leveraging message-passing neural networks (MPNNs) to propagate local infor...
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| Veröffentlicht in: | Electronics (Basel) Jg. 14; H. 3; S. 423 |
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| Abstract | We propose SAT-GATv2, a graph neural network (GNN)-based model designed to solve the Boolean satisfiability problem (SAT) through graph-based deep learning techniques. SAT-GATv2 transforms SAT formulas into graph structures, leveraging message-passing neural networks (MPNNs) to propagate local information and dynamic attention mechanisms (GATv2) to accurately capture inter-node dependencies and enhance node feature representations. Unlike traditional heuristic-driven SAT solvers, SAT-GATv2 adopts a data-driven approach, learning structural patterns directly from graph representations and providing a complementary framework to existing methods. Experimental results demonstrate that SAT-GATv2 achieves an accuracy improvement of 1.75–5.51% over NeuroSAT on challenging random 3-SAT(n) instances, highlighting its effectiveness in handling difficult problem distributions, and outperforms other GNN-based models on SR(n) datasets, showcasing its scalability and adaptability. Ablation studies validate the critical roles of MPNNs and GATv2 in improving prediction accuracy and scalability. While SAT-GATv2 does not yet surpass CDCL-based solvers in overall performance, it addresses their limitations in scalability and adaptability to complex instances, offering an efficient graph-based alternative for tackling larger and more complex SAT problems. This study establishes a foundation for integrating deep learning with combinatorial optimization, emphasizing its potential for applications in artificial intelligence and operations research. |
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| AbstractList | We propose SAT-GATv2, a graph neural network (GNN)-based model designed to solve the Boolean satisfiability problem (SAT) through graph-based deep learning techniques. SAT-GATv2 transforms SAT formulas into graph structures, leveraging message-passing neural networks (MPNNs) to propagate local information and dynamic attention mechanisms (GATv2) to accurately capture inter-node dependencies and enhance node feature representations. Unlike traditional heuristic-driven SAT solvers, SAT-GATv2 adopts a data-driven approach, learning structural patterns directly from graph representations and providing a complementary framework to existing methods. Experimental results demonstrate that SAT-GATv2 achieves an accuracy improvement of 1.75–5.51% over NeuroSAT on challenging random 3-SAT(n) instances, highlighting its effectiveness in handling difficult problem distributions, and outperforms other GNN-based models on SR(n) datasets, showcasing its scalability and adaptability. Ablation studies validate the critical roles of MPNNs and GATv2 in improving prediction accuracy and scalability. While SAT-GATv2 does not yet surpass CDCL-based solvers in overall performance, it addresses their limitations in scalability and adaptability to complex instances, offering an efficient graph-based alternative for tackling larger and more complex SAT problems. This study establishes a foundation for integrating deep learning with combinatorial optimization, emphasizing its potential for applications in artificial intelligence and operations research. |
| Audience | Academic |
| Author | Chang, Wenjing Liu, Wenlong |
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| Cites_doi | 10.1145/368273.368557 10.24963/ijcai.2020/164 10.1007/s11633-022-1396-2 10.1145/3534678.3542609 10.1007/978-3-319-24318-4_29 10.1613/jair.1.15956 10.3233/FAIA336 10.1613/jair.2490 10.1109/TNN.2008.2005605 10.1145/3308558.3313562 10.1109/IJCNN55064.2022.9892733 10.1007/s44196-022-00139-9 10.1016/j.aiopen.2021.01.001 10.1007/978-3-030-24258-9_24 10.1145/3491210 10.1007/s10479-010-0693-2 10.22492/issn.2435-7030.2021.11 10.1007/978-3-030-58475-7_51 10.1109/JPROC.2015.2455034 10.1109/ICCAD57390.2023.10323731 10.20944/preprints202409.0452.v1 10.1007/978-3-540-68279-0 10.1109/TNNLS.2020.2978386 10.3233/FAIA200987 |
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| References | Cameron (ref_21) 2020; 34 ref_50 ref_11 Vizel (ref_7) 2015; 103 Zhou (ref_38) 2020; 1 Wu (ref_39) 2020; 32 ref_51 ref_19 ref_18 ref_17 ref_16 ref_15 Guo (ref_12) 2023; 20 Scarselli (ref_41) 2008; 20 ref_25 ref_24 Liu (ref_33) 2024; 37 ref_29 ref_28 ref_27 ref_26 Alyahya (ref_34) 2023; 55 Hoos (ref_48) 2000; 2000 ref_36 ref_32 ref_31 ref_30 Kurin (ref_23) 2020; 33 Davis (ref_10) 1962; 5 ref_37 Paterson (ref_9) 1990; Volume 443 ref_47 ref_46 ref_45 ref_44 ref_43 ref_42 Schidler (ref_2) 2024; 80 Simonis (ref_49) 2020; Volume 12333 ref_40 ref_1 ref_3 Wu (ref_35) 2021; 34 Heule (ref_13) 2015; Volume 9340 Janota (ref_22) 2019; Volume 11628 Xu (ref_14) 2008; 32 Chang (ref_20) 2022; 15 ref_5 ref_4 Horbach (ref_8) 2010; 181 ref_6 |
| References_xml | – ident: ref_5 – volume: 5 start-page: 394 year: 1962 ident: ref_10 article-title: A machine program for theorem-proving publication-title: Commun. ACM doi: 10.1145/368273.368557 – ident: ref_32 – ident: ref_26 – ident: ref_51 – volume: 34 start-page: 13266 year: 2021 ident: ref_35 article-title: Representing long-range context for graph neural networks with global attention publication-title: Adv. Neural Inf. Process. Syst. – ident: ref_42 – ident: ref_1 – ident: ref_30 doi: 10.24963/ijcai.2020/164 – volume: 20 start-page: 640 year: 2023 ident: ref_12 article-title: Machine learning methods in solving the boolean satisfiability problem publication-title: Mach. Intell. Res. doi: 10.1007/s11633-022-1396-2 – ident: ref_37 doi: 10.1145/3534678.3542609 – volume: 37 start-page: 16264 year: 2024 ident: ref_33 article-title: Can graph neural networks learn to solve the MaxSAT problem?(student abstract) publication-title: Proc. AAAI Conf. Artif. Intell. – ident: ref_31 – ident: ref_27 – volume: Volume 9340 start-page: 405 year: 2015 ident: ref_13 article-title: Evaluating CDCL Variable Scoring Schemes publication-title: Theory and Applications of Satisfiability Testing—SAT 2015 doi: 10.1007/978-3-319-24318-4_29 – ident: ref_45 – volume: 80 start-page: 875 year: 2024 ident: ref_2 article-title: SAT-based decision tree learning for large data sets publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.1.15956 – ident: ref_4 doi: 10.3233/FAIA336 – volume: 32 start-page: 565 year: 2008 ident: ref_14 article-title: SATzilla: Portfolio-based algorithm selection for SAT publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.2490 – volume: 20 start-page: 61 year: 2008 ident: ref_41 article-title: The graph neural network model publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2008.2005605 – ident: ref_46 doi: 10.1145/3308558.3313562 – ident: ref_24 – ident: ref_17 doi: 10.1109/IJCNN55064.2022.9892733 – ident: ref_40 – volume: 15 start-page: 84 year: 2022 ident: ref_20 article-title: Predicting Propositional Satisfiability Based on Graph Attention Networks publication-title: Int. J. Comput. Intell. Syst. doi: 10.1007/s44196-022-00139-9 – volume: 1 start-page: 57 year: 2020 ident: ref_38 article-title: Graph neural networks: A review of methods and applications publication-title: AI Open doi: 10.1016/j.aiopen.2021.01.001 – volume: Volume 11628 start-page: 336 year: 2019 ident: ref_22 article-title: Guiding High-Performance SAT Solvers with Unsat-Core Predictions publication-title: Theory and Applications of Satisfiability Testing—SAT 2019 doi: 10.1007/978-3-030-24258-9_24 – volume: 55 start-page: 1 year: 2023 ident: ref_34 article-title: On the Structure of the Boolean Satisfiability Problem: A Survey publication-title: ACM Comput. Surv., Mar. doi: 10.1145/3491210 – ident: ref_18 – volume: 34 start-page: 3324 year: 2020 ident: ref_21 article-title: Predicting propositional satisfiability via end-to-end learning publication-title: Proc. AAAI Conf. Artif. Intell. – ident: ref_44 – volume: 2000 start-page: 283 year: 2000 ident: ref_48 article-title: SATLIB: An online resource for research on SAT publication-title: Sat – volume: 181 start-page: 89 year: 2010 ident: ref_8 article-title: A Boolean satisfiability approach to the resource-constrained project scheduling problem publication-title: Ann. Oper. Res. doi: 10.1007/s10479-010-0693-2 – ident: ref_6 – ident: ref_25 – ident: ref_50 – ident: ref_29 – ident: ref_28 doi: 10.22492/issn.2435-7030.2021.11 – volume: Volume 12333 start-page: 885 year: 2020 ident: ref_49 article-title: Learning the Satisfiability of Pseudo-Boolean Problem with Graph Neural Networks publication-title: Principles and Practice of Constraint Programming doi: 10.1007/978-3-030-58475-7_51 – volume: 103 start-page: 2021 year: 2015 ident: ref_7 article-title: Boolean satisfiability solvers and their applications in model checking publication-title: Proc. IEEE doi: 10.1109/JPROC.2015.2455034 – ident: ref_16 doi: 10.1109/ICCAD57390.2023.10323731 – volume: 33 start-page: 9608 year: 2020 ident: ref_23 article-title: Can q-learning with graph networks learn a generalizable branching heuristic for a sat solver? publication-title: Adv. Neural Inf. Process. Syst. – ident: ref_15 – ident: ref_36 – ident: ref_19 – ident: ref_43 – ident: ref_47 doi: 10.20944/preprints202409.0452.v1 – ident: ref_3 doi: 10.1007/978-3-540-68279-0 – volume: Volume 443 start-page: 446 year: 1990 ident: ref_9 article-title: Local optimization and the Traveling Salesman Problem publication-title: Automata, Languages and Programming – volume: 32 start-page: 4 year: 2020 ident: ref_39 article-title: A comprehensive survey on graph neural networks publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2020.2978386 – ident: ref_11 doi: 10.3233/FAIA200987 |
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| SubjectTerms | Ablation Accuracy Adaptability Algorithms Architecture Artificial intelligence Boolean Combinatorial analysis Computer science Deep learning Design Efficiency Graph neural networks Graphical representations Heuristic Innovations Machine learning Management science Message passing Neural networks Solvers Traveling salesman problem Variables |
| Title | SAT-GATv2: A Dynamic Attention-Based Graph Neural Network for Solving Boolean Satisfiability Problem |
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