Abstract
Recent work introduced an effective method for extraction of reduced unsatisfiable cores of CNF formulas as a by-product of validation of clausal proofs emitted by conflict-driven clause learning SAT solvers. In this paper, we demonstrate that this method for trimming CNF formulas can also benefit state-of-the-art tools for the computation of a Minimal Unsatisfiable Subformula (MUS). Furthermore, we propose a number of techniques that improve the quality of trimming, and demonstrate a significant positive impact on the performance of MUS extractors from the improved trimming.
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
Preview
Unable to display preview. Download preview PDF.
References
Marques-Silva, J., Janota, M., Belov, A.: Minimal sets over monotone predicates in boolean formulae. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 592–607. Springer, Heidelberg (2013)
Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Communications 25(2), 97–116 (2012)
Nadel, A., Ryvchin, V., Strichman, O.: Efficient MUS extraction with resolution. In: [24], pp.197–200
Audemard, G., Lagniez, J.M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: Application to MUS extraction, In: [25], pp. 309–317
Lagniez, J.M., Biere, A.: Factoring out assumptions to speed up MUS extraction. In: [25], pp. 276–292
Dershowitz, N., Hanna, Z., Nadel, A.: A scalable algorithm for minimal unsatisfiable core extraction. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 36–41. Springer, Heidelberg (2006)
Zhang, L., Malik, S.: Validating SAT solvers using an independent resolution-based checker: Practical implementations and other applications. In: DATE, pp. 10880–10885. IEEE Computer Society (2003)
Belov, A., Marques-Silva, J.: MUSer2: An efficient MUS extractor. Journal of Satisfiability 8, 123–128 (2012)
Wieringa, S., Heljanko, K.: Asynchronous multi-core incremental SAT solving. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 139–153. Springer, Heidelberg (2013)
Goldberg, E.I., Novikov, Y.: Verification of proofs of unsatisfiability for CNF formulas. In: DATE, pp. 10886–10891 (2003)
Heule, M.J.H., Hunt Jr., W.A., Wetzler, N.: Trimming while checking clausal proofs, In: [24], pp. 181–188
Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)
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)
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 (2009)
Van Gelder, A.: Verifying RUP proofs of propositional unsatisfiability. In: ISAIM (2008)
Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning 40(1), 1–33 (2008)
Nadel, A.: Boosting minimal unsatisfiable core extraction. In: FMCAD, pp. 121–128 (October 2010)
Kullmann, O., Lynce, I., Marques-Silva, J.: Categorisation of clauses in conjunctive normal forms: Minimally unsatisfiable sub-clause-sets and the lean kernel. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 22–35. Springer, Heidelberg (2006)
Marques-Silva, J., Lynce, I.: On improving MUS extraction algorithms. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 159–173. Springer, Heidelberg (2011)
Marques-Silva, J.: Minimal unsatisfiability: Models, algorithms and applications. In: ISMVL, pp. 9–14 (2010)
Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)
Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Boutilier, C. (ed.) IJCAI, pp. 399–404 (2009)
Jussila, T., Sinz, C., Biere, A.: Extended resolution proofs for symbolic SAT solving with quantification. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 54–60. Springer, Heidelberg (2006)
Formal Methods in Computer-Aided Design, FMCAD 2013, Portland, OR, USA, October 20-23. IEEE (2013)
Järvisalo, M., Van Gelder, A. (eds.): SAT 2013. LNCS, vol. 7962. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Belov, A., Heule, M.J.H., Marques-Silva, J. (2014). MUS Extraction Using Clausal Proofs. In: Sinz, C., Egly, U. (eds) Theory and Applications of Satisfiability Testing – SAT 2014. SAT 2014. Lecture Notes in Computer Science, vol 8561. Springer, Cham. https://doi.org/10.1007/978-3-319-09284-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-09284-3_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09283-6
Online ISBN: 978-3-319-09284-3
eBook Packages: Computer ScienceComputer Science (R0)