Skip to main content
SpringerLink
Log in

Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API

  • Conference paper
  • First Online:
Theory and Applications of Satisfiability Testing -- SAT 2015 (SAT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9340))

Abstract

We consider the incremental computation of minimal unsatisfiable cores (MUCs) of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a novel API to allow for incremental solving based on clause groups. A clause group is a set of clauses which is incrementally added to or removed from a previously solved QBF. Our implementation of the novel API is related to incremental SAT solving based on selector variables and assumptions. However, the API entirely hides selector variables and assumptions from the user, which facilitates the integration of DepQBF in other tools. We present implementation details and, for the first time, report on experiments related to the computation of MUCs of QBFs using DepQBF’s novel clause group API.

Supported by the Austrian Science Fund (FWF) under grant S11409-N23. We would like to thank Aina Niemetz and Mathias Preiner for helpful discussions.

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
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. Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Efficient generation of unsatisfiability proofs and cores in SAT. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 16–30. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Commun. 25(2), 97–116 (2012)

    MathSciNet  MATH  Google Scholar 

  4. Benedetti, M., Mangassarian, H.: QBF-based formal verification: experience and perspectives. JSAT 5, 133–191 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 101–115. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An algorithm to evaluate quantified boolean formulae and its experimental evaluation. J. Autom. Reasoning 28(2), 101–142 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cimatti, A., Griggio, A., Sebastiani, R.: A simple and flexible way of computing small unsatisfiable cores in SAT modulo theories. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 334–339. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)

    Article  MATH  Google Scholar 

  11. Egly, U., Kronegger, M., Lonsing, F., Pfandler, A.: Conformant planning as a case study of incremental QBF solving. In: Aranda-Corral, G.A., Calmet, J., Martín-Mateos, F.J. (eds.) AISC 2014. LNCS, vol. 8884, pp. 120–131. Springer, Heidelberg (2014)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  13. Grégoire, É., Mazure, B., Piette, C.: On Approaches to Explaining Infeasibility of Sets of Boolean Clauses. In: ICTAI, pp. 74–83. IEEE Computer Society (2008)

    Google Scholar 

  14. Ignatiev, A., Janota, M., Marques-Silva, J.: Quantified maximum satisfiability. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 250–266. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Jussila, T., Biere, A.: Compressing BMC encodings with QBF. ENTCS 174(3), 45–56 (2007)

    MATH  Google Scholar 

  16. Kleine Büning, H., Zhao, X.: Minimal false quantified boolean formulas. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 339–352. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Lagniez, J.-M., Biere, A.: Factoring out assumptions to speed Up MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 276–292. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Letz, R.: Lemma and model caching in decision procedures for quantified boolean formulas. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, p. 160. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  20. Lonsing, F., Egly, U.: Incremental QBF solving. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 514–530. Springer, Heidelberg (2014)

    Google Scholar 

  21. Lonsing, F., Egly, U.: Incremental QBF solving by DepQBF. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 307–314. Springer, Heidelberg (2014)

    Google Scholar 

  22. Lonsing, F., Egly, U.: Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API. CoRR abs/1502.02484 (2015). http://arxiv.org/abs/1502.02484, SAT 2015 proceedings version (6-page tool paper) with appendix

  23. Marin, P., Miller, C., Lewis, M.D.T., Becker, B.: Verification of Partial Designs using Incremental QBF Solving. In: Rosenstiel, W., Thiele, L. (eds.) DATE, pp. 623–628. IEEE (2012)

    Google Scholar 

  24. Marques-Silva, J.: Minimal unsatisfiability: models, algorithms and applications (Invited Paper). In: ISMVL, pp. 9–14. IEEE Computer Society (2010)

    Google Scholar 

  25. 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)

    Chapter  Google Scholar 

  26. Miller, C., Marin, P., Becker, B.: Verification of partial designs using incremental QBF. AI Commun. 28(2), 283–307 (2015)

    MathSciNet  Google Scholar 

  27. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: DAC, pp. 530–535. ACM (2001)

    Google Scholar 

  28. Nadel, A.: Boosting Minimal Unsatisfiable Core Extraction. In: Bloem, R., Sharygina, N. (eds.) FMCAD, pp. 221–229. IEEE (2010)

    Google Scholar 

  29. Nadel, A., Ryvchin, V., Strichman, O.: Accelerated deletion-based extraction of minimal unsatisfiable cores. JSAT 9, 27–51 (2014)

    MathSciNet  Google Scholar 

  30. Nadel, A., Ryvchin, V., Strichman, O.: Ultimately incremental SAT. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 206–218. Springer, Heidelberg (2014)

    Google Scholar 

  31. Yu, Y., Malik, S.: Validating the result of a Quantified Boolean Formula (QBF) solver: theory and practice. In: Tang, T. (ed.) ASP-DAC, pp. 1047–1051. ACM Press (2005)

    Google Scholar 

  32. Zhang, L., Malik, S.: Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, p. 200. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Knowledge-Based Systems Group Vienna University of Technology, Vienna, Austria

    Florian Lonsing & Uwe Egly

Authors
  1. Florian Lonsing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Uwe Egly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Florian Lonsing .

Editor information

Editors and Affiliations

  1. Algorithms, University of Texas, Austin, Texas, USA

    Marijn Heule

  2. Trusted Systems Research Group, Fort Meade, Texas, USA

    Sean Weaver

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Lonsing, F., Egly, U. (2015). Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API. In: Heule, M., Weaver, S. (eds) Theory and Applications of Satisfiability Testing -- SAT 2015. SAT 2015. Lecture Notes in Computer Science(), vol 9340. Springer, Cham. https://doi.org/10.1007/978-3-319-24318-4_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24318-4_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24317-7

  • Online ISBN: 978-3-319-24318-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation