Advertisement

Abstract

We consider the problem of incrementally solving a sequence of quantified Boolean formulae (QBF). Incremental solving aims at using information learned from one formula in the process of solving the next formulae in the sequence. Based on a general overview of the problem and related challenges, we present an approach to incremental QBF solving which is application-independent and hence applicable to QBF encodings of arbitrary problems. We implemented this approach in our incremental search-based QBF solver DepQBF and report on implementation details. Experimental results illustrate the potential benefits of incremental solving in QBF-based workflows.

Keywords

Boolean Formula Wall Clock Time Selector Variable Bound Model Check Push Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Balabanov, V., Jiang, J.R.: Unified QBF certification and its applications. Formal Methods in System Design 41(1), 45–65 (2012)CrossRefMATHGoogle Scholar
  3. 3.
    Becker, B., Ehlers, R., Lewis, M.D.T., Marin, P.: ALLQBF Solving by Computational Learning. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 370–384. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Benedetti, M., Mangassarian, H.: QBF-Based Formal Verification: Experience and Perspectives. JSAT 5, 133–191 (2008)MathSciNetGoogle Scholar
  5. 5.
    Biere, A.: PicoSAT Essentials. JSAT 4(2-4), 75–97 (2008)MATHGoogle Scholar
  6. 6.
    Bloem, R., Könighofer, R., Seidl, M.: SAT-Based Synthesis Methods for Safety Specs. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 1–20. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  7. 7.
    Büning, H.K., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Inf. Comput. 117(1), 12–18 (1995)CrossRefMATHGoogle Scholar
  8. 8.
    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)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Cashmore, M., Fox, M., Giunchiglia, E.: Planning as Quantified Boolean Formula. In: Raedt, L.D., Bessière, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., Lucas, P.J.F. (eds.) ECAI. Frontiers in Artificial Intelligence and Applications, pp. 217–222. IOS Press (2012)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Eén, N., Sörensson, N.: Temporal Induction by Incremental SAT Solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)CrossRefGoogle Scholar
  12. 12.
    Egly, U., Kronegger, M., Lonsing, F., Pfandler, A.: Conformant Planning as a Case Study of Incremental QBF Solving. CoRR abs/1405.7253 (2014)Google Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    Goultiaeva, A., Van Gelder, A., Bacchus, F.: A Uniform Approach for Generating Proofs and Strategies for Both True and False QBF Formulas. In: Walsh, T. (ed.) IJCAI, pp. 546–553. IJCAI/AAAI (2011)Google Scholar
  15. 15.
    Goultiaeva, A., Bacchus, F.: Recovering and Utilizing Partial Duality in QBF. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 83–99. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    Goultiaeva, A., Seidl, M., Biere, A.: Bridging the Gap between Dual Propagation and CNF-based QBF Solving. In: Macii, E. (ed.) DATE, pp. 811–814. EDA Consortium. ACM DL, San Jose (2013)Google Scholar
  17. 17.
    Hillebrecht, S., Kochte, M.A., Erb, D., Wunderlich, H.J., Becker, B.: Accurate QBF-Based Test Pattern Generation in Presence of Unknown Values. In: Macii, E. (ed.) DATE, pp. 436–441. EDA Consortium, ACM DL, San Jose, CA, USA (2013)Google Scholar
  18. 18.
    Janota, M., Grigore, R., Marques-Silva, J.: On QBF Proofs and Preprocessing. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 473–489. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  19. 19.
    Klieber, W., Sapra, S., Gao, S., Clarke, E.M.: A Non-prenex, Non-clausal QBF Solver with Game-State Learning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 128–142. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  20. 20.
    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)CrossRefGoogle Scholar
  21. 21.
    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, pp. 160–175. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  22. 22.
    Lonsing, F., Biere, A.: Integrating Dependency Schemes in Search-Based QBF Solvers. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 158–171. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Lonsing, F., Egly, U.: Incremental QBF Solving by DepQBF (Extended Abstract). In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 307–314. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  24. 24.
    Lonsing, F., Egly, U., Van Gelder, A.: Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 100–115. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  25. 25.
    Mangassarian, H., Veneris, A.G., Benedetti, M.: Robust QBF Encodings for Sequential Circuits with Applications to Verification, Debug, and Test. IEEE Trans. Computers 59(7), 981–994 (2010)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Marin, P., Miller, C., Becker, B.: Incremental QBF Preprocessing for Partial Design Verification - (Poster Presentation). In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 473–474. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  27. 27.
    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
  28. 28.
    Nadel, A., Ryvchin, V.: Efficient SAT Solving under Assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    Niemetz, A., Preiner, M., Lonsing, F., Seidl, M., Biere, A.: Resolution-Based Certificate Extraction for QBF - (Tool Presentation). In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 430–435. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  30. 30.
    Samulowitz, H., Davies, J., Bacchus, F.: Preprocessing QBF. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 514–529. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  31. 31.
    Seidl, M., Könighofer, R.: Partial witnesses from preprocessed quantified Boolean formulas. In: DATE, pp. 1–6. IEEE (2014)Google Scholar
  32. 32.
    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, FAIA, vol. 185, pp. 131–153. IOS Press (2009)Google Scholar
  33. 33.
    Staber, S., Bloem, R.: Fault Localization and Correction with QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 355–368. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  34. 34.
    Sülflow, A., Fey, G., Drechsler, R.: Using QBF to Increase Accuracy of SAT-Based Debugging. In: ISCAS, pp. 641–644. IEEE (2010)Google Scholar
  35. 35.
    Van Gelder, A.: Primal and Dual Encoding from Applications into Quantified Boolean Formulas. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 694–707. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  36. 36.
    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, pp. 200–215. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Florian Lonsing
    • 1
  • Uwe Egly
    • 1
  1. 1.Institute of Information Systems, Knowledge-Based Systems GroupVienna University of TechnologyViennaAustria

Personalised recommendations