Skip to main content
SpringerLink
Log in

Finding Guaranteed MUSes Fast

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2008 (SAT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4996))

Abstract

We introduce an algorithm for finding a minimal unsatisfiable subset (MUS) of a CNF formula. We have implemented and evaluated the algorithm and found that its performance is very competitive on a wide range of benchmarks, including both formulas that are close to minimal unsatisfiable and formulas containing MUSes that are only a small fraction of the formula size.

In our simple but effective algorithm we associate assignments with clauses. The notion of associated assignment has emerged from our work on a Brouwer’s fixed point approximation algorithm applied to satisfiability. There, clauses are regarded to be entities that order the set of assignments and that can select an assignment to be associated with them, resulting in a Pareto optimal agreement.

In this presentation we abandon all terminology from this theory which is superfluous with respect to the recent objective and make the paper self contained.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Nam, G.J., Sakallah, K.A., Rutenbar, R.A.: Satisfiability-based layout revisited: Detailed routing of complex FPGAs vis search-based Boolean SAT. In: FPGA, pp. 167–175 (1999)

    Google Scholar 

  2. Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) ETAPS 1999 and TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. McMillan, K.L.: Interpolants and symbolic model checking. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 89–90. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Rintanen, J., Heljanko, K., Niemelä, I.: Planning as satisfiability: parallel plans and algorithms for plan search. Artif. Intell. 170(12-13), 1031–1080 (2006)

    Article  MATH  Google Scholar 

  5. Zhang, L., Malik, S.: Extracting Small Unsatisfiable Cores from Unsatisfiable Boolean Formula. In: Theory and Applications of Satisfiability Testing, 6th International Conference, SAT 2003. Santa Margherita Ligure, Italy, May 5-8 (2003)

    Google Scholar 

  6. Oh, Y., Mneimneh, M.N., Andraus, Z.S., Sakallah, K.A., Markov, I.L.: AMUSE: A minimally-unsatisfiable subformula extractor. In: Malik, S., Fix, L., Kahng, A.B. (eds.) DAC, pp. 518–523. ACM, New York (2004)

    Chapter  Google Scholar 

  7. Grégoire, É., Mazure, B., Piette, C.: Local-search extraction of MUSes. Constraints 12(3), 325–344 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lynce, I., Silva, J.P.M.: On computing minimum unsatisfiable cores. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, Springer, Heidelberg (2005)

    Google Scholar 

  9. Liffiton, M.H., Sakallah, K.A.: On finding all minimally unsatisfiable subformulas [25], 173–186

    Google Scholar 

  10. Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. Journal of Automated Reasoning 40(1), 1–33 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wieringa, S.: Finding cores using a Brouwer’s fixed point approximation algorithm. Master’s thesis, Delft University of Technology, Faculty of EWI (2007)

    Google Scholar 

  12. van Maaren, H.: Pivoting algorithms based on Boolean vector labeling. Acta Mathematica Vietnamica 22(1), 183–198 (1997)

    MathSciNet  MATH  Google Scholar 

  13. Kullmann, O., Lynce, I., Marques-Silva, J.: Categorisation of clauses in conjunctive normal forms: Minimally unsatisfiable sub-clause-sets and the lean kernel. [24] 22–35

    Google Scholar 

  14. 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)

    Google Scholar 

  15. Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. [15] 61–75

    Google Scholar 

  16. Tamiz, M., Mardle, S.J., Jones, D.F.: Detecting IIS in infeasible linear programmes using techniques from goal programming. Computers & OR 23(2), 113–119 (1996)

    Article  MATH  Google Scholar 

  17. Galinier, P., Hertz, A.: Solution techniques for the large set covering problem. Discrete Applied Mathematics 155(3), 312–326 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. de Siqueira, N.J.L., Puget, J.-F.: Explanation-based generalisation of failures. In: ECAI, pp. 339–344 (1988)

    Google Scholar 

  19. Dershowitz, N., Hanna, Z., Nadel, A.: A scalable algorithm for minimal unsatisfiable core extraction. [24] 36–41

    Google Scholar 

  20. Huang, J.: MUP: A minimal unsatisfiability prover. In: Tang, T.A. (ed.) ASP-DAC, pp. 432–437. ACM Press, New York (2005)

    Chapter  Google Scholar 

  21. Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult instances of Boolean satisfiability in the presence of symmetry. IEEE Trans. on CAD of Integrated Circuits and Systems 22(9), 1117–1137 (2003)

    Article  Google Scholar 

  22. Darwiche, A.: New advances in compiling CNF into decomposable negation normal form. In: de Mántaras, R.L., Saitta, L. (eds.) ECAI, pp. 328–332. IOS Press, Amsterdam (2004)

    Google Scholar 

  23. Aloul, F.A., Markov, I.L., Sakallah, K.A.: MINCE: A static global variable-ordering heuristic for SAT search and BDD manipulation. J. UCS 10(12), 1562–1596 (2004)

    Google Scholar 

  24. Biere, A., Gomes, C.P. (eds.): SAT 2006. LNCS, vol. 4121. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  25. Bacchus, F., Walsh, T. (eds.): SAT 2005. LNCS, vol. 3569. Springer, Heidelberg (2005)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of EWI, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    Hans van Maaren

  2. Department of Information and Computer Science, Helsinki University of Technology (TKK), P.O. Box 5400, FI-02015, TKK, Finland

    Siert Wieringa

Authors
  1. Hans van Maaren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Siert Wieringa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hans Kleine Büning Xishun Zhao

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van Maaren, H., Wieringa, S. (2008). Finding Guaranteed MUSes Fast. In: Kleine Büning, H., Zhao, X. (eds) Theory and Applications of Satisfiability Testing – SAT 2008. SAT 2008. Lecture Notes in Computer Science, vol 4996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79719-7_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-79719-7_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79718-0

  • Online ISBN: 978-3-540-79719-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation