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Constraints

, Volume 14, Issue 1, pp 80–116 | Cite as

A self-adaptive multi-engine solver for quantified Boolean formulas

  • Luca Pulina
  • Armando Tacchella
Article

Abstract

In this paper we study the problem of engineering a robust solver for quantified Boolean formulas (QBFs), i.e., a tool that can efficiently solve formulas across different problem domains without the need for domain-specific tuning. The paper presents two main empirical results along this line of research. Our first result is the development of a multi-engine solver, i.e., a tool that selects among its reasoning engines the one which is more likely to yield optimal results. In particular, we show that syntactic QBF features can be correlated to the performances of existing QBF engines across a variety of domains. We also show how a multi-engine solver can be obtained by carefully picking state-of-the-art QBF solvers as basic engines, and by harnessing inductive reasoning techniques to learn engine-selection policies. Our second result is the improvement of our multi-engine solver with the capability of updating the learned policies when they fail to give good predictions. In this way the solver becomes also self-adaptive, i.e., able to adjust its internal models when the usage scenario changes substantially. The rewarding results obtained in our experiments show that our solver AQME—Adaptive QBF Multi-Engine—can be more robust and efficient than state-of-the-art single-engine solvers, even when it is confronted with previously uncharted formulas and competitors.

Keywords

Self-adaptive multi-engine solver Quantified Boolean formulas AQME 

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References

  1. 1.
    Aha, D., & Kibler, D. (1991). Instance-based learning algorithms. Machine Learning, 6, 37–66.Google Scholar
  2. 2.
    Ansotegui, C., Gomes, C. P., & Selman, B. (2005). Achille’s heel of QBF. In Proc. of AAAI (pp. 275–281).Google Scholar
  3. 3.
    Benedetti, M. (2005). sKizzo: A suite to evaluate and certify QBFs. In 20th int’l. conference on automated deduction, Lecture notes in computer science (Vol. 3632, pp. 369–376). Springer.Google Scholar
  4. 4.
    Biere, A. (2005). Resolve and expand. In Seventh intl. conference on theory and applications of satisfiability testing (SAT’04), LNCS (Vol. 3542, pp. 59–70).Google Scholar
  5. 5.
    Castellini, C., Giunchiglia, E., & Tacchella, A. (2003). SAT-based planning in complex domains: Concurrency, constraints and nondeterminism. Artificial Intelligence, 147, 85–117.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Cohen, W. W. (1995). Fast effective rule induction. In Twelfth international conference on machine learning (pp. 115–123).Google Scholar
  7. 7.
    Davis, M., Logemann, G., Loveland, D. (1962). A machine program for theorem proving. Communications of the ACM, 5(7), 394–397.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Egly, U., Eiter, T., Tompits, H., & Woltran, S. (2000). Solving advanced reasoning tasks using quantified Boolean formulas. In Seventeenth national conference on artificial intelligence (AAAI 2000) (pp. 417–422). The MIT Press.Google Scholar
  9. 9.
    Gebruers, C., Hnich, B., Bridge, D. G., & Freuder, E. C. (2005). Using CBR to select solution strategies in constraint programming. In Proceedings of the 6th int.l conf. of case-based reasoning, research and development (ICCBR 2005) (pp. 222–236).Google Scholar
  10. 10.
    Gent, I. P., Nightingale, P., & Rowley, A. (2004). Encoding quantified CSPs as quantified Boolean formulae. In Proceedings of the 16th European conference on artificial intelligence (ECAI 2004) (pp. 176–180).Google Scholar
  11. 11.
    Gent, I. P., & Rowley, A. G. D. (2003). Encoding connect 4 using quantified Boolean formulae. Technical Report APES-68-2003, APES Research Group, July.Google Scholar
  12. 12.
    Giunchiglia, E., Narizzano, M., & Tacchella, A. (2001). Quantified Boolean formulas satisfiability library (QBFLIB). www.qbflib.org.
  13. 13.
    Gomes, C. P., & Selman, B. (2001). Algorithm portfolios. Artificial Intelligence, 126, 43–62.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Hanna, Z., Dershowitz, N., & Katz, J. (2005). Bounded model checking with QBF. In Eight international conference on theory and applications of satisfiability testing (SAT 2005), Lecture notes in computer science (Vol. 3569, pp. 408–414). Springer.Google Scholar
  15. 15.
    Herbstritt, M., Becker, B., & Scholl, C. (2006). Advanced SAT-techniques for bounded model checking of blackbox designs. In MTV workshop (pp. 37–44).Google Scholar
  16. 16.
    Huberman, B. A., Lukose, R. M., & Hogg, T. (1997). An economics approach to hard computational problems. Science, 275, 51–54.CrossRefGoogle Scholar
  17. 17.
    Jussila, T., & Biere, A. (2006). Compressing BMC encodings with QBF. In Proc. 4th intl. workshop on bounded model checking (BMC’06).Google Scholar
  18. 18.
    Kaufman, L., & Rousseeeuw, P. J. (1990). Finding groups in Data. Wiley.Google Scholar
  19. 19.
    Kleine-Büning, H., Karpinski, M., & Flögel, A. (1995). Resolution for quantified Boolean formulas. Information and Computation, 117(1), 12–18.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Kohavi, R. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proc. of int’l joint conference on artificial intelligence (IJCAI) (pp. 1137–1145).Google Scholar
  21. 21.
    Le Cessie, S., & van Houwelingen, J. C. (1992). Ridge estimators in logistic regression. Applied Statistics, 41, 191–201.zbMATHCrossRefGoogle Scholar
  22. 22.
    Lobjois, L., & Lemaître, M. (1998). Branch and bound algorithm selection by performance prediction. In Proceedings of 15th nat’l conf. on artificial intelligence (AAAI 1998) (pp. 353–358).Google Scholar
  23. 23.
    Mneimneh, M., & Sakallah, K. (2003). Computing vertex eccentricity in exponentially large graphs: QBF formulation and solution. In Sixth international conference on theory and applications of satisfiability testing (SAT 2003), Lecture notes in computer science (Vol. 2919, pp. 411–425). Springer.Google Scholar
  24. 24.
    Mitchell, D. G., Selman, B., & Levesque, H. J. (1992). Hard and easy distributions for SAT problems. In Proceedings of the tenth national conference on artificial intelligence (pp. 459–465). AAAI Press.Google Scholar
  25. 25.
    Narizzano, M., Pulina, L., & Taccchella, A. (2006). QBF solvers competitive evaluation (QBFEVAL). http://www.qbflib.org/qbfeval.
  26. 26.
    Narizzano, M., Pulina, L., & Tacchella, A. (2006). The third QBF solvers comparative evaluation. Journal on Satisfiability, Boolean Modeling and Computation, 2, 145–164. Available on-line at http://jsat.ewi.tudelft.nl/.zbMATHGoogle Scholar
  27. 27.
    Narizzano, M., Pulina, L., & Tacchella, A. (2006). The QBFEVAL web portal. In 10th European conference on logics in artificial intelligence (JELIA 2006), Lecture notes in computer science (Vol. 4160, pp. 494–497). Springer.Google Scholar
  28. 28.
    Narizzano, M., Pulina, L., & Tacchella, A. (2007). Ranking and reputation sytems in the QBF competition. In 10th conference of the Italian association for artificial intelligence (AI*IA 2007), Lecture notes in artificial intelligence (Vol. 4733, pp. 97–108). Springer.Google Scholar
  29. 29.
    Narizzano, M., & Tacchella, A. (2005). QDIMACS prenex CNF standard ver. 1.1. Available online from http://www.qbflib.org/qdimacs.html.
  30. 30.
    Nudelman, E., Devku, A., Shoham, Y., & Leyton-Brown, K. (2004). Understanding random SAT: Beyond the clauses-to-variables ratio. In 10th intl conference on principles and practice of constraint programming (CP2004), LNCS (Vol. 3258, pp. 438–452). Springer.Google Scholar
  31. 31.
    Nudelman, E., Leyton-Brown, K., Devkar, A., Shoham, Y., & Hoos, H. (2004). SATzilla: An algorithm portfolio for SAT. In In seventh international conference on theory and applications of satisfiability testing, SAT 2004 competition: Solver descriptions (pp. 13–14).Google Scholar
  32. 32.
    Pan, G., & Vardi, M. Y. (2003). Optimizing a BDD-based modal solver. In Proceedings of the 19th international conference on automated deduction, Lecture notes in computer science (Vol. 2741, pp. 75–89). Springer.Google Scholar
  33. 33.
    Papadimitriou, C. H. (1994). Computational complexity. Addison-Wesley.Google Scholar
  34. 34.
    Pulina, L., & Tacchella, A. (2007). A multi-engine solver for quantified Boolean formulas. In 13th conference on principles and practice of constraint programming (CP 2007), Lecture notes in computer science (Vol. 4741, pp. 574–589). Springer.Google Scholar
  35. 35.
    Quinlan, J. R. (1993). C4.5: Programs for machine learning. Morgan Kaufmann Publishers.Google Scholar
  36. 36.
    Rintanen, J. (2001). Partial implicit unfolding in the Davis-Putnam procedure for quantified Boolean formulae. In Proc. LPAR, LNCS (Vol. 2250, pp. 362–376).Google Scholar
  37. 37.
    Samulowitz, H., & Memisevic, R. (2007). Learning to solve QBF. In In proc. of 22nd conference on artificial intelligence (AAAI’07) (pp. 255–260).Google Scholar
  38. 38.
    Stéphan, I. (2006). Boolean propagation based on literals for quantified Boolean formulae. In Proceedings of 17th European conf. on artificial intelligence (ECAI 2006) (pp. 452–456).Google Scholar
  39. 39.
    Stockmeyer, L. J., & Meyer, A. R. (1973). Word problems requiring exponential time. In 5th annual ACM symposium on the theory of computation (pp. 1–9).Google Scholar
  40. 40.
    Streeter, M. J., Golovin, D., & Smith, S. F. (2007). Restart schedules for ensembles of problem instances. In Proceedings of 22nd AAAI conference on artificial intelligence (AAAI 2007) (pp. 1204–1210).Google Scholar
  41. 41.
    Turner, H. (2002). Polynomial-length planning spans the polynomial hierarchy. In Proc. of eighth European conf. on logics in artificial intelligence (JELIA’02), Lecture notes in artificial intelligence (Vol. 2424, pp. 111–124). Springer.Google Scholar
  42. 42.
    Witten, I. H., & Frank, E. (2005). Data mining (2nd ed.). Morgan Kaufmann.Google Scholar
  43. 43.
    Xu, L., Hoos, H. H., & Leyton-Brown, K. (2007). Hierarchical hardness models for SAT. In 13th conference on principles and practice of constraint programming (CP 2007), Lecture notes in computer science (Vol. 4741, pp. 696–711). Springer.Google Scholar
  44. 44.
    Xu, L., Hutter, F., Hoos, H. H., & Leyton-Brown, K. (2007). The design and analysis of an algorithm portfolio for SAT. In 13th conference on principles and practice of constraint programming (CP 2007), Lecture notes in computer science (Vol. 4741, pp. 712–727). Springer.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.DISTUniversità di GenovaGenovaItaly

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