Abstract
In 2020 Feng & Bacchus revisited variants of the all-UIP learning strategy, which considerably improved performance of their version of CaDiCaL submitted to the SAT Competition 2020, particularly on large planning instances. We improve on their algorithm by tightly integrating this idea with learned clause minimization. This yields a clean shrinking algorithm with complexity linear in the size of the implication graph. It is fast enough to unconditionally shrink learned clauses until completion. We further define trail redundancy and show that our version of shrinking removes all redundant literals. Independent experiments with the three SAT solvers CaDiCaL, Kissat, and Satch confirm the effectiveness of our approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Source code and log files are available at http://fmv.jku.at/sat_shrinking.
References
Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: IJCAI, pp. 399–404 (2009), http://ijcai.org/Proceedings/09/Papers/074.pdf
Biere, A.: CaDiCaL, Lingeling, Plingeling, Treengeling and YalSAT entering the SAT Competition 2018. In: Heule, M., Järvisalo, M., Suda, M. (eds.) Proceedings of of SAT Competition 2018 - Solver and Benchmark Descriptions. Department of Computer Science Series of Publications B, vol. B-2018-1, pp. 13–14. University of Helsinki (2018)
Biere, A.: Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010. Technical Report, FMV Reports Series, Institute for Formal Models and Verification, Johannes Kepler University (August 2021)
Biere, A.: The SAT solver Satch. Git repository (2021). https://github.com/arminbiere/satch Accessed 03 2021
Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling entering the SAT Competition 2020. In: Balyo, T., Froleyks, N., Heule, M., Iser, M., Järvisalo, M., Suda, M. (eds.) Proceedings of SAT Competition 2020 - Solver and Benchmark Descriptions. Department of Computer Science Report Series B, vol. B-2020-1, pp. 51–53. University of Helsinki (2020)
Biere, A., Fröhlich, A.: Evaluating CDCL variable scoring schemes. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 405–422. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24318-4_29
Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)
Cherkassky, B.V., Goldberg, A.V., Silverstein, C.: Buckets, heaps, lists, and monotone priority queues. SIAM J. Comput. 28(4), 1326–1346 (1999). https://doi.org/10.1137/S0097539796313490
Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional Horn formulae. J. Log. Program. 1(3), 267–284 (1984). https://doi.org/10.1016/0743-1066(84)90014-1
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
Feng, N., Bacchus, F.: Clause size reduction with all-UIP learning. In: Pulina, L., Seidl, M. (eds.) SAT 2020. LNCS, vol. 12178, pp. 28–45. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51825-7_3
Fleury, M.: Formalization of logical calculi in Isabelle/HOL. Ph.D. thesis, Saarland University, Saarbrücken, Germany (2020). https://tel.archives-ouvertes.fr/tel-02963301
Fleury, M., Biere, A.: Efficient all-UIP learned clause minimization (extended version). Technical Report. 21/3, Johannes Kepler University Linz, FMV Reports Series, Institute for Formal Models and Verification, Johannes Kepler University, Altenbergerstr. 69, 4040 Linz, Austria (2021). https://doi.org/10.350/fmvtr.2021-3
Hickey, R., Feng, N., Bacchus, F.: Cadical-trail, Cadical-alluip, Cadical-alluip-trail and maple-LCM-dist-alluip-trail at the SAT competition. In: Balyo, T., Froleyks, N., Heule, M., Iser, M., Järvisalo, M., Suda, M. (eds.) Proceedings of SAT Competition 2020 - Solver and Benchmark Descriptions. Department of Computer Science Report Series B, vol. B-2020-1, p. 10. University of Helsinki (2020)
Möhle, S., Biere, A.: Backing backtracking. In: Janota, M., Lynce, I. (eds.) SAT 2019. LNCS, vol. 11628, pp. 250–266. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-24258-9_18
Nadel, A., Ryvchin, V.: Chronological backtracking. In: Beyersdorff, O., Wintersteiger, C.M. (eds.) SAT 2018. LNCS, vol. 10929, pp. 111–121. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94144-8_7
Silva, J.P.M., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 131–153. IOS Press (2009). https://doi.org/10.3233/978-1-58603-929-5-131
Sörensson, N., Biere, A.: Minimizing learned clauses. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 237–243. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_23
Gelder, A.: Improved conflict-clause minimization leads to improved propositional proof traces. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 141–146. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_15
Gelder, A.: Generalized conflict-clause strengthening for satisfiability solvers. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 329–342. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21581-0_26
Zhang, L., Madigan, C.F., Moskewicz, M.W., Malik, S.: Efficient conflict driven learning in Boolean satisfiability solver. In: ICCAD, pp. 279–285. IEEE Computer Society (2001). https://doi.org/10.1109/ICCAD.2001.968634
Acknowledgment
This work is supported by Austrian Science Fund (FWF), NFN S11408-N23 (RiSE), and the LIT AI Lab funded by the State of Upper Austria. We also thank Sibylle Möhle and the anonymous reviewers for suggesting textual improvements.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Fleury, M., Biere, A. (2021). Efficient All-UIP Learned Clause Minimization. In: Li, CM., Manyà, F. (eds) Theory and Applications of Satisfiability Testing – SAT 2021. SAT 2021. Lecture Notes in Computer Science(), vol 12831. Springer, Cham. https://doi.org/10.1007/978-3-030-80223-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-80223-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-80222-6
Online ISBN: 978-3-030-80223-3
eBook Packages: Computer ScienceComputer Science (R0)