Abstract
Incremental SAT is about solving a sequence of related SAT problems efficiently. It makes use of already learned information to avoid repeating redundant work. Also preprocessing and inprocessing are considered to be crucial. Our calculus uses the most general redundancy property and extends existing inprocessing rules to incremental SAT solving. It allows to automatically reverse earlier simplification steps, which are inconsistent with literals in new incrementally added clauses. Our approach to incremental SAT solving not only simplifies the use of inprocessing but also substantially improves solving time.
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References
Audemard, G., Lagniez, J.-M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: application to MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39071-5_23
Balyo, T., Biere, A., Iser, M., Sinz, C.: SAT race 2015. Artif. Intell. 241, 45–65 (2016)
Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24605-3_37
Hooker, J.N.: Solving the incremental satisfiability problem. J. Log. Program. 15(1&2), 177–186 (1993)
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
Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18275-4_7
Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)
Kupferschmid, S., Lewis, M.D.T., Schubert, T., Becker, B.: Incremental preprocessing methods for use in BMC. Form. Methods Syst. Des. 39(2), 185–204 (2011)
Gocht, S., Balyo, T.: Accelerating SAT based planning with incremental SAT solving. In: Barbulescu, L., Frank, J., Mausam, Smith, S.F. (eds.) Proceedings of the 27th International Conference on Automated Planning and Scheduling, ICAPS 2017, pp. 135–139. AAAI Press (2017)
Martins, R., Joshi, S., Manquinho, V.M., Lynce, I.: On using incremental encodings in unsatisfiability-based MaxSAT solving. JSAT 9, 59–81 (2014)
Nadel, A.: Boosting minimal unsatisfiable core extraction. In: Bloem, R., Sharygina, N. (eds.) Proceedings of 10th International Conference on Formal Methods in Computer-Aided Design, FMCAD 2010, pp. 221–229. IEEE (2010)
Sebastiani, R.: Lazy satisability modulo theories. JSAT 3(3–4), 141–224 (2007)
Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24605-3_26
Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005). https://doi.org/10.1007/11499107_5
Heule, M.J.H., Järvisalo, M., Biere, A.: Efficient CNF simplification based on binary implication graphs. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 201–215. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21581-0_17
Järvisalo, M., Biere, A., Heule, M.J.H.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12002-2_10
Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 355–370. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31365-3_28
Järvisalo, M., Biere, A.: Reconstructing solutions after blocked clause elimination. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 340–345. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14186-7_30
Nadel, A., Ryvchin, V., Strichman, O.: Preprocessing in incremental SAT. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 256–269. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31612-8_20
Heule, M.J.H., Kiesl, B., Biere, A.: Short proofs without new variables. In: de Moura, L. (ed.) CADE 2017. LNCS (LNAI), vol. 10395, pp. 130–147. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63046-5_9
Heule, M.J.H., Kiesl, B., Biere, A.: Strong extension-free proof systems. J. Autom. Reason. (2019). https://doi.org/10.1007/s10817-019-09516-0
Audemard, G., Katsirelos, G., Simon, L.: A restriction of extended resolution for clause learning sat solvers. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI 2010). AAAI Press (2010)
Kullmann, O.: On a generalization of extended resolution. Discret. Appl. Math. 96–97, 149–176 (1999)
Manthey, N., Heule, M.J.H., Biere, A.: Automated reencoding of Boolean formulas. In: Biere, A., Nahir, A., Vos, T. (eds.) HVC 2012. LNCS, vol. 7857, pp. 102–117. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39611-3_14
Nadel, A., Ryvchin, V., Strichman, O.: Ultimately incremental SAT. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 206–218. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_16
Nadel, A., Ryvchin, V.: Efficient SAT solving under assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31612-8_19
Blanchette, J.C., Fleury, M., Lammich, P., Weidenbach, C.: A verified SAT solver framework with learn, forget, restart, and incrementality. J. Autom. Reason. 61(1–4), 333–365 (2018)
Fazekas, K., Bacchus, F., Biere, A.: Implicit hitting set algorithms for maximum satisfiability modulo theories. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds.) IJCAR 2018. LNCS (LNAI), vol. 10900, pp. 134–151. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94205-6_10
Balyo, T., Fröhlich, A., Heule, M.J.H., Biere, A.: Everything you always wanted to know about blocked sets (but were afraid to ask). In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 317–332. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_24
Biere, A.: Yet another local search solver and Lingeling and friends entering the SAT competition 2014. In: Balint, A., Belov, A., Heule, M.J.H., Järvisalo, M. (eds.) SAT Competition 2014. Department of Computer Science Series of Publications B, pp. 39–40. University of Helsinki (2014)
Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified Boolean formulas. Inf. Process. Lett. 8(3), 121–123 (1979)
Brafman, R.I.: A simplifier for propositional formulas with many binary clauses. In: Nebel, B. (ed.) Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001, Morgan Kaufmann, pp. 515–522 (2001)
Biere, A.: CaDiCaL, Lingeling, Plingeling, Treengeling and YalSAT entering the SAT competition 2018. In: Heule, M.J.H., Järvisalo, M., Suda, M. (eds.) Proceedings of SAT Competition 2018 - Solver and Benchmark Descriptions. Volume B-2018-1 of Department of Computer Science Series of Publications B, pp. 13–14. University of Helsinki (2018)
Luo, M., Li, C., Xiao, F., Manyà, F., Lü, Z.: An effective learnt clause minimization approach for CDCL SAT solvers. In: Sierra, C. (ed.) Proceedings of the 26th International Joint Conference on Artificial Intelligence, IJCAI 2017, pp. 703–711. ijcai.org (2017)
Piette, C., Hamadi, Y., Sais, L.: Vivifying propositional clausal formulae. In: Ghallab, M., Spyropoulos, C.D., Fakotakis, N., Avouris, N.M. (eds.) Proceedings of the 18th European Conference on Artificial Intelligence, ECAI 2008. Volume 178 of Frontiers in Artificial Intelligence and Applications, pp. 525–529. IOS Press (2008)
Schwartz, E.J., Avgerinos, T., Brumley, D.: All you ever wanted to know about dynamic taint analysis and forward symbolic execution (but might have been afraid to ask). In: 31st IEEE Symposium on Security and Privacy, S&P 2010, 16–19 May 2010, pp. 317–331. IEEE Computer Society, Berleley/Oakland (2010)
Biere, A., Heljanko, K., Wieringa, S.: AIGER 1.9 and beyond. Technical report, FMV reports series, Institute for Formal Models and Verification, Johannes Kepler University, Altenbergerstr. 69, 4040 Linz, Austria (2011)
Biere, A., van Dijk, T., Heljanko, K.: Hardware model checking competition 2017. In: Stewart, D., Weissenbacher, G. (eds.) Formal Methods in Computer Aided Design, FMCAD 2017, p. 9. IEEE (2017)
Jussila, T., Biere, A.: Compressing BMC encodings with QBF. Electr. Notes Theor. Comput. Sci. 174(3), 45–56 (2007)
Heule, M.J.H., Järvisalo, M., Biere, A.: Revisiting hyper binary resolution. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 77–93. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38171-3_6
Kuehlmann, A., Paruthi, V., Krohm, F., Ganai, M.K.: Robust Boolean reasoning for equivalence checking and functional property verification. IEEE Trans CAD Integr. Circ. Syst. 21(12), 1377–1394 (2002)
Brummayer, R., Biere, A.: Local two-level and-inverter graph minimization without blowup. In: Proceedings of the 2nd Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS 2006) (2006)
Niemetz, A., Preiner, M., Wolf, C., Biere, A.: Btor2, BtorMC and Boolector 3.0. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 587–595. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_32
Balyo, T., Heule, M.J.H., Järvisalo, M. (eds.): Proceedings of SAT Competition 2016 - Solver and Benchmark Descriptions. Volume B-2016-1 of Department of Computer Science Series of Publications B. University of Helsinki (2016)
Balyo, T., Heule, M.J.H., Järvisalo, M., (eds.): Proceedings of SAT Competition 2017 - Solver and Benchmark Descriptions. Volume B-2017-1 of Department of Computer Science Series of Publications B. University of Helsinki (2017)
Audemard, G., Simon, L.: Glucose and syrup in the SAT 2017. In: Balyo, T., Heule, M.J.H., Järvisalo, M. (eds.) Proceedings of SAT Competition 2017 - Solver and Benchmark Descriptions. Volume B-2017-1 of Department of Computer Science Series of Publications B, pp. 16–17. University of Helsinki (2017)
Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244–257. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_24
Manthey, N.: Riss 7. In Balyo, T., Heule, M.J.H., Järvisalo, M., (eds.) Proceedings of SAT Competition 2017 - Solver and Benchmark Descriptions. Volume B-2017-1 of Department of Computer Science Series of Publications B, p. 29. University of Helsinki (2017)
Han, H., Somenzi, F.: Alembic: an efficient algorithm for CNF preprocessing. In: Proceedings of the 44th Design Automation Conference, DAC 2007, pp. 582–587. IEEE (2007)
Acknowledgments
This research has been supported by the Austrian Science Fund (FWF) under projects W1255-N23 and S11408-N23. We thank Mathias Preiner and Aina Niemetz for their help in experimenting with Boolector and Håkan Hjort for providing feedback on using an incremental version of CaDiCaL.
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Fazekas, K., Biere, A., Scholl, C. (2019). Incremental Inprocessing in SAT Solving. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_9
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