BFS-Based Symmetry Breaking Predicates for DFA Identification

  • Vladimir Ulyantsev
  • Ilya Zakirzyanov
  • Anatoly Shalyto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)

Abstract

It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be translated to Boolean satisfiability (SAT). Modern SAT-solvers can efficiently tackle hard DFA identification instances. We present a technique to reduce SAT search space by enforcing an enumeration of DFA states in breadth-first search (BFS) order. We propose symmetry breaking predicates, which can be added to Boolean formulae representing various DFA identification problems. We show how to apply this technique to DFA identification from both noiseless and noisy data. The main advantage of the proposed approach is that it allows to exactly determine the existence or non-existence of a solution of the noisy DFA identification problem.

Keywords

Grammatical inference Boolean satisfiability Learning automata Symmetry breaking techniques 

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References

  1. 1.
    Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (2006)Google Scholar
  2. 2.
    De La Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognition 38(9), 1332–1348 (2005)CrossRefGoogle Scholar
  3. 3.
    Gold, E.M.: Complexity of automaton identification from given data. Information and Control 37(3), 302–320 (1978)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Pitt, L., Warmuth, M.K.: The minimum consistent DFA problem cannot be approximated within any polynomial. Journal of the ACM 40(1), 95–142 (1993)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Lang, K.J., Pearlmutter, B.A., Price, R.A.: Results of the abbadingo one DFA learning competition and a new evidence-driven state merging algorithm. In: Honavar, V.G., Slutzki, G. (eds.) ICGI 1998. LNCS (LNAI), vol. 1433, pp. 1–112. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  6. 6.
    Lang, K.J.: Faster Algorithms for Finding Minimal Consistent DFAs. Technical report (1999)Google Scholar
  7. 7.
    Bugalho, M., Oliveira, A.L.: Inference of regular languages using state merging algorithms with search. Pattern Recognition 38(9), 1457–1467 (2005)CrossRefMATHGoogle Scholar
  8. 8.
    Dupont, P.: Regular grammatical inference from positive and negative samples by genetic search: the GIG method. In: Carrasco, R.C., Oncina, J. (eds.) ICGI 1994. LNCS, vol. 862, pp. 236–2445. Springer, Heidelberg (1994) CrossRefGoogle Scholar
  9. 9.
    Luke, S., Hamahashi, S., Kitano, H.: Genetic programming. In: Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 1098–1105 (1999)Google Scholar
  10. 10.
    Lucas, S.M., Reynolds, T.J.: Learning DFA: evolution versus evidence driven state merging. In: The 2003 Congress on Evolutionary Computation, CEC 2003, vol. 1, pp. 351–358. IEEE (2003)Google Scholar
  11. 11.
    Lucas, S.: GECCO 2004 noisy DFA results. In: GECCO Proc. (2004)Google Scholar
  12. 12.
    Lucas, S.M., Reynolds, T.J.: Learning deterministic finite automata with a smart state labeling evolutionary algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(7), 1063–1074 (2005)CrossRefGoogle Scholar
  13. 13.
    Heule, M.J.H., Verwer, S.: Exact DFA identification using SAT solvers. In: Sempere, J.M., García, P. (eds.) ICGI 2010. LNCS, vol. 6339, pp. 66–79. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  14. 14.
    Walkinshaw, N., Lambeau, B., Damas, C., Bogdanov, K., Dupont, P.: STAMINA: a competition to encourage the development and assessment of software model inference techniques. Empirical Software Engineering 18(4), 791–824 (2013)CrossRefGoogle Scholar
  15. 15.
    Biere, A., Heule, M., van Maaren, H.: Handbook of satisfiability, vol. 185. IOS Press (2009)Google Scholar
  16. 16.
    Amla, N., Du, X., Kuehlmann, A., Kurshan, R.P., McMillan, K.L.: An analysis of SAT-based model checking techniques in an industrial environment. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 254–268. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  17. 17.
    Lohfert, R., Lu, J.J., Zhao, D.: Solving SQL constraints by incremental translation to SAT. In: Nguyen, N.T., Borzemski, L., Grzech, A., Ali, M. (eds.) IEA/AIE 2008. LNCS (LNAI), vol. 5027, pp. 669–676. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  18. 18.
    Galeotti, J.P., Rosner, N., Lopez Pombo, C.G., Frias, M.F.: TACO: Efficient SAT-Based Bounded Verification Using Symmetry Breaking and Tight Bounds. IEEE Transactions on Software Engineering 39(9), 1283–1307 (2013)Google Scholar
  19. 19.
    Ulyantsev, V., Tsarev, F.: Extended finite-state machine induction using SAT-solver. In: Proc. of ICMLA 2011, vol. 2, pp. 346–349. IEEE (2011)Google Scholar
  20. 20.
    Lambeau, B., Damas, C., Dupont, P.E.: State-merging DFA induction algorithms with mandatory merge constraints. In: Clark, A., Coste, F., Miclet, L. (eds.) ICGI 2008. LNCS (LNAI), vol. 5278, pp. 139–153. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  21. 21.
    Chambers, L.D.: Practical handbook of genetic algorithms: complex coding systems, vol. 3. CRC Press (2010)Google Scholar
  22. 22.
    Barahona, P., Hölldobler, S., Nguyen, V.: Efficient SAT-encoding of linear csp constraints. In: 13th International Symposium on Artificial Intelligence and Mathematics-ISAIM, Fort Lauderdale, Florida, USA (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Vladimir Ulyantsev
    • 1
  • Ilya Zakirzyanov
    • 1
  • Anatoly Shalyto
    • 1
  1. 1.ITMO UniversitySaint-PetersburgRussia

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