Conformant Planning as a Case Study of Incremental QBF Solving

  • Uwe Egly
  • Martin Kronegger
  • Florian Lonsing
  • Andreas Pfandler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8884)


We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase and in the solving phase. Experimental results show that incremental QBF solving outperforms non-incremental QBF solving. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.


Optimal Plan Planning Tool Boolean Formula Bounded Model Check Conformant Planning 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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.H.R.: Unified QBF certification and its applications. Formal Methods in System Design 41(1), 45–65 (2012)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baral, C., Kreinovich, V., Trejo, R.: Computational Complexity of Planning and Approximate Planning in the Presence of Incompleteness. Artificial Intelligence 122(1-2), 241–267 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Biere, A.: Resolve and Expand. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 6.
    Blum, A., Furst, M.L.: Fast Planning Through Planning Graph Analysis. Artificial Intelligence 90(1-2), 281–300 (1997)CrossRefzbMATHGoogle Scholar
  7. 7.
    Bubeck, U., Kleine Büning, H.: Bounded Universal Expansion for Preprocessing QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 244–257. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation. Journal of Automated Reasoning 28(2), 101–142 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem-proving. Communications of the ACM 5(7), 394–397 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Eén, N., Sörensson, N.: Temporal Induction by Incremental SAT Solving. Electronic Notes in Theoretical Computer Science 89(4), 543–560 (2003)CrossRefGoogle Scholar
  11. 11.
    Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas. Journal of Artificial Intelligence Research 26, 371–416 (2006)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Giunchiglia, E., Marin, P., Narizzano, M.: sQueezeBF: An Effective Preprocessor for QBFs Based on Equivalence Reasoning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 85–98. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    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. AAAI Press (2011)Google Scholar
  14. 14.
    Heule, M., Seidl, M., Biere, A.: A Unified Proof System for QBF Preprocessing. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 91–106. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  15. 15.
    Hoffmann, J., Brafman, R.I.: Conformant planning via heuristic forward search: A new approach. Artificial Intelligence 170(6-7), 507–541 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    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
  17. 17.
    Kleine Büning, H., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Information and Computation 117(1), 12–18 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Kronegger, M., Pfandler, A., Pichler, R.: Conformant planning as a benchmark for QBF-solvers. In: Report Int. Workshop on Quantified Boolean Formulas (QBF 2013). pp. 1–5 (2013),
  19. 19.
    Kupferschmid, S., Lewis, M.D.T., Schubert, T., Becker, B.: Incremental Preprocessing Methods for Use in BMC. Formal Methods in System Design 39(2), 185–204 (2011)CrossRefzbMATHGoogle 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.: Nenofex: Expanding NNF for QBF Solving. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 196–210. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Lonsing, F., Egly, U.: Incremental QBF Solving. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 514–530. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    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
  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., Strichman, O.: Ultimately Incremental SAT. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 206–218. Springer, Heidelberg (2014)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.
    Palacios, H., Geffner, H.: Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width. Journal of Artificial Intelligence Research 35, 623–675 (2009)zbMATHMathSciNetGoogle Scholar
  31. 31.
    Rintanen, J.: Asymptotically Optimal Encodings of Conformant Planning in QBF. In: Holte, R.C., Howe, A.E. (eds.) AAAI, pp. 1045–1050. AAAI Press (2007)Google Scholar
  32. 32.
    Seidl, M., Könighofer, R.: Partial witnesses from preprocessed quantified Boolean formulas. In: DATE, pp. 1–6. IEEE (2014)Google Scholar
  33. 33.
    Smith, D.E., Weld, D.S.: Conformant Graphplan. In: Mostow, J., Rich, C. (eds.) AAAI/IAAI, pp. 889–896. AAAI Press / The MIT Press (1998)Google Scholar
  34. 34.
    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

  • Uwe Egly
    • 1
  • Martin Kronegger
    • 1
  • Florian Lonsing
    • 1
  • Andreas Pfandler
    • 1
    • 2
  1. 1.Institute of Information SystemsVienna University of TechnologyAustria
  2. 2.School of Economic DisciplinesUniversity of SiegenGermany

Personalised recommendations