Skip to main content

Minimizing Models for Tseitin-Encoded SAT Instances

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2013 (SAT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7962))

Abstract

Many applications of SAT solving can profit from minimal models—a partial variable assignment that is still a witness for satisfiability. Examples include software verification, model checking, and counterexample-guided abstraction refinement. In this paper, we examine how a given model can be minimized for SAT instances that have been obtained by Tseitin encoding of a full propositional logic formula. Our approach uses a SAT solver to efficiently minimize a given model, focusing on only the input variables. Experiments show that some models can be reduced by over 50 percent.

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

Access this chapter

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. SAT-Race 2010 (2010), http://baldur.iti.uka.de/sat-race-2010/ (accessed February 14, 2013)

  2. Ben-Eliyahu, R., Dechter, R.: On computing minimal models. Ann. Math. Artif. Intell. 18(1), 3–27 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boy de la Tour, T.: An optimality result for clause form translation. J. Symb. Comput. 14(4), 283–301 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dennis, G., Chang, F.S.-H., Jackson, D.: Modular verification of code with SAT. In: International Symposium in Software Testing and Analysis (ISSTA 2006), pp. 109–120 (2006)

    Google Scholar 

  5. Dillig, I., Dillig, T., McMillan, K.L., Aiken, A.: Minimum satisfying assignments for SMT. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 394–409. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  6. Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast decision procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/term resolution and learning in the evaluation of quantified boolean formulas. J. Artif. Intell. Res. (JAIR 2006) 26, 371–416 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Groce, A., Kroening, D.: Making the most of BMC counterexamples. Electr. Notes Theor. Comput. Sci. 119(2), 67–81 (2005)

    Article  Google Scholar 

  9. Jackson, P., Sheridan, D.: Clause form conversions for boolean circuits. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 183–198. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Miyuki Koshimura, H.F., Nabeshima, H., Hasegawa, R.: Minimal model generation with respect to an atom set. In: International Workshop on First-Order Theorem Proving (FTP 2009), pp. 49–59 (2009)

    Google Scholar 

  11. Nopper, T., Scholl, C., Becker, B.: Computation of minimal counterexamples by using black box techniques and symbolic methods. In: Intl. Conf. on Computer-Aided Design (ICCAD 2007), pp. 273–280 (2007)

    Google Scholar 

  12. Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. J. Symb. Comput. 2(3), 293–304 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ravi, K., Somenzi, F.: Minimal assignments for bounded model checking. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 31–45. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Shen, S., Qin, Y., Li, S.: Minimizing counterexample with unit core extraction and incremental SAT. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 298–312. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Sinz, C.: Towards an optimal CNF encoding of boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Torlak, E., Jackson, D.: Kodkod: A relational model finder. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 632–647. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Slisenko, A.O. (ed.) Studies in Constructive Mathematics and Mathematical Logic, pp. 115–125 (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Iser, M., Sinz, C., Taghdiri, M. (2013). Minimizing Models for Tseitin-Encoded SAT Instances. In: Järvisalo, M., Van Gelder, A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39071-5_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39071-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39070-8

  • Online ISBN: 978-3-642-39071-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics