Abstract
Many satisfiability problems exhibit symmetry properties. Thus, the development of symmetry exploitation techniques seems a natural way to try to improve the efficiency of solvers by preventing them from exploring isomorphic parts of the search space. These techniques can be classified into two categories: dynamic and static symmetry breaking. Static approaches have often appeared to be more effective than dynamic ones. But although these approaches can be considered as complementary, very few works have tried to combine them.
In this paper, we present a new tool, CosySEL, that implements a composition of the static Effective Symmetry Breaking Predicates (esbp) technique with the dynamic Symmetric Explanation Learning (sel). esbp exploits symmetries to prune the search tree and sel uses symmetries to speed up the tree traversal. These two accelerations are complementary and their combination was made possible by the introduction of Local symmetries.
We conduct our experiments on instances issued from the last ten sat competitions and the results show that our tool outperforms the existing tools on highly symmetrical problems.
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Notes
- 1.
Such a small set typically does not form a group, i.e., is not closed under composition, but closing it under composition generates a detected symmetry group for the formula.
- 2.
- 3.
Cosy library is released under GPL v3 license at https://github.com/lip6/cosy.
- 4.
github.com/jheusser/satcoin.
- 5.
We recall that CosySP is based of MiniSAT, and the comparison with the other tools is not totally fair!.
References
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult sat instances in the presence of symmetry. In: Proceedings 2002 Design Automation Conference (IEEE Cat. No. 02CH37324) pp. 731–736. IEEE (2002)
Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient symmetry breaking for Boolean satisfiability. IEEE Trans. Comput. 55(5), 549–558 (2006)
Atserias, A., Lauria, M., Nordström, J.: Narrow proofs may be maximally long. ACM Trans. Comput. Logic (TOCL) 17(3), 1–30 (2016)
Atserias, A., Müller, M., Oliva, S.: Lower bounds for DNF-refutations of a relativized weak pigeonhole principle. J. Symbolic Logic 80(2), 450–476 (2015)
Audemard, G., Simon, L.: Predicting learnt clauses quality in modern sat solvers. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, pp. 399–404 (2009)
Benhamou, B., Nabhani, T., Ostrowski, R., Saïdi, M.R.: Enhancing clause learning by symmetry in sat solvers. In: 2010 22nd IEEE International Conference on Tools with Artificial Intelligence, vol. 1, pp. 329–335. IEEE (2010)
Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49059-0_14
Biere, A., Heule, M., van Maaren, H.: Handbook of Satisfiability, vol. 185. IOS press, Amsterdam (2009)
Cherif, M.S., Habet, D., Terrioux, C.: Kissat MAB: combining VSIDS and CHB through multi-armed bandit. SAT Competition 2021, 15 (2021)
Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking predicates for search problems. KR 96(1996), 148–159 (1996)
Devriendt, J., Bogaerts, B., Bruynooghe, M.: Symmetric explanation learning: effective dynamic symmetry handling for SAT. In: Gaspers, S., Walsh, T. (eds.) SAT 2017. LNCS, vol. 10491, pp. 83–100. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66263-3_6
Devriendt, J., Bogaerts, B., Bruynooghe, M., Denecker, M.: Improved static symmetry breaking for SAT. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 104–122. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_8
Devriendt, J., Bogaerts, B., De Cat, B., Denecker, M., Mears, C.: Symmetry propagation: Improved dynamic symmetry breaking in SAT. In: 2012 IEEE 24th International Conference on Tools with Artificial Intelligence, vol. 1, pp. 49–56. IEEE (2012)
Elffers, J., Nordström, J.: Documentation of some combinatorial benchmarks. Proc. SAT Competition 2016, 67–69 (2016)
Giunchiglia, F., Sebastiani, R.: Building decision procedures for modal logics from propositional decision procedures—the case study of modal K. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 583–597. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61511-3_115
Järvisalo, M., Le Berre, D., Roussel, O., Simon, L.: The international sat solver competitions. AI Mag. 33(1), 89–92 (2012)
Junttila, T., Kaski, P.: Engineering an efficient canonical labeling tool for large and sparse graphs. In: Applegate, D., Brodal, G.S., Panario, D., Sedgewick, R. (eds.) Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithms and Combinatorics, pp. 135–149. SIAM (2007)
Katebi, H., Sakallah, K.A., Markov, I.L.: Symmetry and satisfiability: an update. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 113–127. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14186-7_11
Kautz, H.A., Selman, B., et al.: Planning as satisfiability. In: ECAI, vol. 92, pp. 359–363 (1992)
Luks, E.M., Roy, A.: The complexity of symmetry-breaking formulas. Ann. Math. Artif. Intell. 41(1), 19–45 (2004)
Manthey, N., Heusser, J.: Satcoin-bitcoin mining via SAT. SAT Competition 2018, 67 (2018)
Massacci, F., Marraro, L.: Logical cryptanalysis as a sat problem. J. Autom. Reasoning 24(1), 165–203 (2000)
Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: introducing effective symmetry breaking in SAT solving. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10805, pp. 99–114. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89960-2_6
Metin, H., Baarir, S., Kordon, F.: Composing symmetry propagation and effective symmetry breaking for SAT solving. In: Badger, J.M., Rozier, K.Y. (eds.) NFM 2019. LNCS, vol. 11460, pp. 316–332. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20652-9_21
Sabharwal, A.: Symchaff: exploiting symmetry in a structure-aware satisfiability solver. Constraints 14(4), 478–505 (2009)
Shtrichman, O.: Tuning SAT checkers for bounded model checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 480–494. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_36
Shtrichman, O.: Pruning techniques for the SAT-based bounded model checking problem. In: Margaria, T., Melham, T. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 58–70. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44798-9_4
Tang, D., Malik, S., Gupta, A., Ip, C.N.: Symmetry reduction in SAT-based model checking. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 125–138. Springer, Heidelberg (2005). https://doi.org/10.1007/11513988_12
Tchinda, R.K., Tayou Djamegni, C.: Enhancing static symmetry breaking with dynamic symmetry handling in CDCL SAT solvers. Int. J. Artif. Intell. Tools 28(03), 1950011 (2019)
Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Siekmann, J.H., Wrightson, G. (eds.) Automation of reasoning, pp. 466–483. Springer, Heidelberg (1983). https://doi.org/10.1007/978-3-642-81955-1_28
Wang, C., Jin, H., Hachtel, G.D., Somenzi, F.: Refining the SAT decision ordering for bounded model checking. In: Proceedings of the 41st Annual Design Automation Conference, pp. 535–538 (2004)
Zhang, X., Cai, S., Chen, Z.: Improving cdcl via local search. SAT Competition 2021, 42 (2021)
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Saouli, S., Baarir, S., Dutheillet, C., Devriendt, J. (2023). CosySEL: Improving SAT Solving Using Local Symmetries. In: Dragoi, C., Emmi, M., Wang, J. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2023. Lecture Notes in Computer Science, vol 13881. Springer, Cham. https://doi.org/10.1007/978-3-031-24950-1_12
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