Predicting the satisfiability of Boolean formulas by incorporating gated recurrent unit (GRU) in the Transformer framework
The Boolean satisfiability (SAT) problem exhibits different structural features in various domains. Neural network models can be used as more generalized algorithms that can be learned to solve specific problems based on different domain data than traditional rule-based approaches. How to accurately...
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| Vydané v: | PeerJ. Computer science Ročník 10; s. e2169 |
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| Abstract | The Boolean satisfiability (SAT) problem exhibits different structural features in various domains. Neural network models can be used as more generalized algorithms that can be learned to solve specific problems based on different domain data than traditional rule-based approaches. How to accurately identify these structural features is crucial for neural networks to solve the SAT problem. Currently, learning-based SAT solvers, whether they are end-to-end models or enhancements to traditional heuristic algorithms, have achieved significant progress. In this article, we propose TG-SAT, an end-to-end framework based on Transformer and gated recurrent neural network (GRU) for predicting the satisfiability of SAT problems. TG-SAT can learn the structural features of SAT problems in a weakly supervised environment. To capture the structural information of the SAT problem, we encodes a SAT problem as an undirected graph and integrates GRU into the Transformer structure to update the node embeddings. By computing cross-attention scores between literals and clauses, a weighted representation of nodes is obtained. The model is eventually trained as a classifier to predict the satisfiability of the SAT problem. Experimental results demonstrate that TG-SAT achieves a 2%–5% improvement in accuracy on random 3-SAT problems compared to NeuroSAT. It also outperforms in SR(N), especially in handling more complex SAT problems, where our model achieves higher prediction accuracy. |
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| AbstractList | The Boolean satisfiability (SAT) problem exhibits different structural features in various domains. Neural network models can be used as more generalized algorithms that can be learned to solve specific problems based on different domain data than traditional rule-based approaches. How to accurately identify these structural features is crucial for neural networks to solve the SAT problem. Currently, learning-based SAT solvers, whether they are end-to-end models or enhancements to traditional heuristic algorithms, have achieved significant progress. In this article, we propose TG-SAT, an end-to-end framework based on Transformer and gated recurrent neural network (GRU) for predicting the satisfiability of SAT problems. TG-SAT can learn the structural features of SAT problems in a weakly supervised environment. To capture the structural information of the SAT problem, we encodes a SAT problem as an undirected graph and integrates GRU into the Transformer structure to update the node embeddings. By computing cross-attention scores between literals and clauses, a weighted representation of nodes is obtained. The model is eventually trained as a classifier to predict the satisfiability of the SAT problem. Experimental results demonstrate that TG-SAT achieves a 2%-5% improvement in accuracy on random 3-SAT problems compared to NeuroSAT. It also outperforms in SR(N), especially in handling more complex SAT problems, where our model achieves higher prediction accuracy.The Boolean satisfiability (SAT) problem exhibits different structural features in various domains. Neural network models can be used as more generalized algorithms that can be learned to solve specific problems based on different domain data than traditional rule-based approaches. How to accurately identify these structural features is crucial for neural networks to solve the SAT problem. Currently, learning-based SAT solvers, whether they are end-to-end models or enhancements to traditional heuristic algorithms, have achieved significant progress. In this article, we propose TG-SAT, an end-to-end framework based on Transformer and gated recurrent neural network (GRU) for predicting the satisfiability of SAT problems. TG-SAT can learn the structural features of SAT problems in a weakly supervised environment. To capture the structural information of the SAT problem, we encodes a SAT problem as an undirected graph and integrates GRU into the Transformer structure to update the node embeddings. By computing cross-attention scores between literals and clauses, a weighted representation of nodes is obtained. The model is eventually trained as a classifier to predict the satisfiability of the SAT problem. Experimental results demonstrate that TG-SAT achieves a 2%-5% improvement in accuracy on random 3-SAT problems compared to NeuroSAT. It also outperforms in SR(N), especially in handling more complex SAT problems, where our model achieves higher prediction accuracy. The Boolean satisfiability (SAT) problem exhibits different structural features in various domains. Neural network models can be used as more generalized algorithms that can be learned to solve specific problems based on different domain data than traditional rule-based approaches. How to accurately identify these structural features is crucial for neural networks to solve the SAT problem. Currently, learning-based SAT solvers, whether they are end-to-end models or enhancements to traditional heuristic algorithms, have achieved significant progress. In this article, we propose TG-SAT, an end-to-end framework based on Transformer and gated recurrent neural network (GRU) for predicting the satisfiability of SAT problems. TG-SAT can learn the structural features of SAT problems in a weakly supervised environment. To capture the structural information of the SAT problem, we encodes a SAT problem as an undirected graph and integrates GRU into the Transformer structure to update the node embeddings. By computing cross-attention scores between literals and clauses, a weighted representation of nodes is obtained. The model is eventually trained as a classifier to predict the satisfiability of the SAT problem. Experimental results demonstrate that TG-SAT achieves a 2%-5% improvement in accuracy on random 3-SAT problems compared to NeuroSAT. It also outperforms in SR(N), especially in handling more complex SAT problems, where our model achieves higher prediction accuracy. |
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| Author | Chang, Wenjing Luo, Junwei Guo, Mengyu |
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| Cites_doi | 10.3390/math10244734 10.1109/ACCESS.2021.3068998 10.1007/978-3-642-81955-1 10.1016/S1574-6526(07)03002-7 10.1016/j.eswa.2022.118241 10.24963/ijcai.2020/164 10.1016/j.2020.07.063 10.1007/BF00339943 10.1007/978-3-030-24258-9_24 10.1016/j.asoc.2022.109312 10.1613/jair.2490 10.3115/v1/D14-1179 10.3233/FAIA200987 10.1016/j.artint.2012.08.001 10.1007/s11633-022-1396-2 10.1016/j.artint.2012.05.004 |
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| Keywords | Deep learning Transformer Cross-attention GRU Boolean satisfiability problem Random 3-SAT |
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| References | Vaswani (10.7717/peerj-cs.2169/ref-29) 2017 Bengio (10.7717/peerj-cs.2169/ref-2) 2021; 290 Karim (10.7717/peerj-cs.2169/ref-13) 2021; 9 Goldberg (10.7717/peerj-cs.2169/ref-9) 2001 Selsam (10.7717/peerj-cs.2169/ref-20) 2019 Danisovszky (10.7717/peerj-cs.2169/ref-6) 2020 Someetheram (10.7717/peerj-cs.2169/ref-27) 2022; 10 Shi (10.7717/peerj-cs.2169/ref-24) 2021 Rintanen (10.7717/peerj-cs.2169/ref-19) 2012; 193 Cook (10.7717/peerj-cs.2169/ref-5) 1971 Kasi (10.7717/peerj-cs.2169/ref-14) 2013 Silva (10.7717/peerj-cs.2169/ref-26) 2021 Sen (10.7717/peerj-cs.2169/ref-22) 2022; 209 Cho (10.7717/peerj-cs.2169/ref-4) 2014 Zhang (10.7717/peerj-cs.2169/ref-33) 2020 Hopfield (10.7717/peerj-cs.2169/ref-12) 1985; 52 Gilmer (10.7717/peerj-cs.2169/ref-8) 2017 Bünz (10.7717/peerj-cs.2169/ref-3) 2017 Xu (10.7717/peerj-cs.2169/ref-30) 2008; 32 Liu (10.7717/peerj-cs.2169/ref-17) 2021 Ozolins (10.7717/peerj-cs.2169/ref-18) 2021 Shi (10.7717/peerj-cs.2169/ref-25) 2022 Selsam (10.7717/peerj-cs.2169/ref-21) 2018 Tseitin (10.7717/peerj-cs.2169/ref-28) 1983 Amizadeh (10.7717/peerj-cs.2169/ref-1) 2018 Yolcu (10.7717/peerj-cs.2169/ref-31) 2019 Zamri (10.7717/peerj-cs.2169/ref-32) 2022; 126 Shi (10.7717/peerj-cs.2169/ref-23) 2021 Guo (10.7717/peerj-cs.2169/ref-11) 2022; 20 Devlin (10.7717/peerj-cs.2169/ref-7) 2008 Gomes (10.7717/peerj-cs.2169/ref-10) 2008; vol. 3 Li (10.7717/peerj-cs.2169/ref-15) 2022 Li (10.7717/peerj-cs.2169/ref-16) 2012; 190 |
| References_xml | – volume: 10 start-page: 4734 issue: 24 year: 2022 ident: 10.7717/peerj-cs.2169/ref-27 article-title: Random maximum 2 satisfiability logic in discrete hopfield neural network incorporating improved election algorithm publication-title: Mathematics doi: 10.3390/math10244734 – volume: 9 start-page: 50831 year: 2021 ident: 10.7717/peerj-cs.2169/ref-13 article-title: Random satisfiability: a higher-order logical approach in discrete hopfield neural network publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3068998 – start-page: 466 volume-title: Automation of reasoning: 2: classical papers on computational logic 1967–1970 year: 1983 ident: 10.7717/peerj-cs.2169/ref-28 article-title: On the complexity of derivation in propositional calculus doi: 10.1007/978-3-642-81955-1 – volume: vol. 3 start-page: 89 volume-title: Handbook of knowledge representation year: 2008 ident: 10.7717/peerj-cs.2169/ref-10 article-title: Satisfiability solvers doi: 10.1016/S1574-6526(07)03002-7 – volume: 209 start-page: 118241 year: 2022 ident: 10.7717/peerj-cs.2169/ref-22 article-title: Toward understanding variations in price and billing in US healthcare services: a predictive analytics approach publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2022.118241 – year: 2020 ident: 10.7717/peerj-cs.2169/ref-33 article-title: NLocalSAT: boosting local search with solution prediction doi: 10.24963/ijcai.2020/164 – volume: 290 start-page: 405 issue: 2 year: 2021 ident: 10.7717/peerj-cs.2169/ref-2 article-title: Machine learning for combinatorial optimization: a methodological tour d’horizon publication-title: European Journal of Operational Research doi: 10.1016/j.2020.07.063 – start-page: 114 year: 2001 ident: 10.7717/peerj-cs.2169/ref-9 article-title: Using SAT for combinational equivalence checking – volume: 52 start-page: 141 year: 1985 ident: 10.7717/peerj-cs.2169/ref-12 article-title: “Neural” computation of decisions in optimization problems publication-title: Biological Cybernetics doi: 10.1007/BF00339943 – year: 2008 ident: 10.7717/peerj-cs.2169/ref-7 article-title: Satisfiability as a classification problem – year: 2019 ident: 10.7717/peerj-cs.2169/ref-20 article-title: Guiding high-performance SAT solvers with unsat-core predictions doi: 10.1007/978-3-030-24258-9_24 – volume: 126 start-page: 109312 year: 2022 ident: 10.7717/peerj-cs.2169/ref-32 article-title: Weighted random k satisfiability for k=1,2 (r2SAT) in discrete hopfield neural network publication-title: Applied Soft Computing doi: 10.1016/j.asoc.2022.109312 – volume: 32 start-page: 565 year: 2008 ident: 10.7717/peerj-cs.2169/ref-30 article-title: SATzilla: portfolio-based algorithm selection for SAT publication-title: Journal of Artificial Intelligence Research doi: 10.1613/jair.2490 – year: 2022 ident: 10.7717/peerj-cs.2169/ref-15 article-title: DeepSAT: an EDA-driven learning framework for SAT – year: 2017 ident: 10.7717/peerj-cs.2169/ref-29 article-title: Attention is all you need – year: 2022 ident: 10.7717/peerj-cs.2169/ref-25 article-title: SATformer: transformers for SAT solving – year: 2021 ident: 10.7717/peerj-cs.2169/ref-17 article-title: Can graph neural networks learn to solve MaxSAT problem? – year: 2017 ident: 10.7717/peerj-cs.2169/ref-3 article-title: Graph neural networks and boolean satisfiability – year: 2021 ident: 10.7717/peerj-cs.2169/ref-24 article-title: Transformers satisfy – start-page: 1 year: 2021 ident: 10.7717/peerj-cs.2169/ref-18 article-title: Goal-aware neural SAT solver – year: 2014 ident: 10.7717/peerj-cs.2169/ref-4 article-title: Learning phrase representations using RNN Encoder–Decoder for statistical machine translation doi: 10.3115/v1/D14-1179 – start-page: 7992 year: 2019 ident: 10.7717/peerj-cs.2169/ref-31 article-title: Learning local search heuristics for Boolean satisfiability – start-page: 151 year: 1971 ident: 10.7717/peerj-cs.2169/ref-5 article-title: The complexity of theorem-proving procedures – year: 2021 ident: 10.7717/peerj-cs.2169/ref-23 article-title: Transformer-based machine learning for fast SAT solvers and logic synthesis – start-page: 732 year: 2013 ident: 10.7717/peerj-cs.2169/ref-14 article-title: Cassandra: proactive conflict minimization through optimized task scheduling – year: 2018 ident: 10.7717/peerj-cs.2169/ref-21 article-title: Learning a SAT solver from single-bit supervision – start-page: 133 volume-title: Handbook of satisfiability year: 2021 ident: 10.7717/peerj-cs.2169/ref-26 article-title: Conflict-driven clause learning SAT solvers doi: 10.3233/FAIA200987 – year: 2018 ident: 10.7717/peerj-cs.2169/ref-1 article-title: Learning to solve circuit-SAT: an unsupervised differentiable approach – volume: 193 start-page: 45 year: 2012 ident: 10.7717/peerj-cs.2169/ref-19 article-title: Planning as satisfiability: heuristics publication-title: Artificial Intelligence doi: 10.1016/j.artint.2012.08.001 – year: 2020 ident: 10.7717/peerj-cs.2169/ref-6 article-title: Classification of SAT problem instances by machine learning methods – year: 2017 ident: 10.7717/peerj-cs.2169/ref-8 article-title: Neural message passing for quantum chemistry – volume: 20 start-page: 640 year: 2022 ident: 10.7717/peerj-cs.2169/ref-11 article-title: Machine learning methods in solving the boolean satisfiability problem publication-title: Machine Intelligence Research doi: 10.1007/s11633-022-1396-2 – volume: 190 start-page: 32 year: 2012 ident: 10.7717/peerj-cs.2169/ref-16 article-title: Optimizing with minimum satisfiability publication-title: Artificial Intelligence doi: 10.1016/j.artint.2012.05.004 |
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| SubjectTerms | Algorithms Algorithms and Analysis of Algorithms Artificial Intelligence Boolean satisfiability problem Computational linguistics Cross-attention Data Mining and Machine Learning Deep learning Electric transformers GRU Language processing Natural language interfaces Neural Networks Random 3-SAT Software Engineering Transformer |
| Title | Predicting the satisfiability of Boolean formulas by incorporating gated recurrent unit (GRU) in the Transformer framework |
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