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BFS-Based Symmetry Breaking Predicates for DFA Identification

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Language and Automata Theory and Applications (LATA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8977))


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.

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  1. Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (2006)

    Google Scholar 

  2. De La Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognition 38(9), 1332–1348 (2005)

    Article  Google Scholar 

  3. Gold, E.M.: Complexity of automaton identification from given data. Information and Control 37(3), 302–320 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  6. Lang, K.J.: Faster Algorithms for Finding Minimal Consistent DFAs. Technical report (1999)

    Google Scholar 

  7. Bugalho, M., Oliveira, A.L.: Inference of regular languages using state merging algorithms with search. Pattern Recognition 38(9), 1457–1467 (2005)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. Lucas, S.: GECCO 2004 noisy DFA results. In: GECCO Proc. (2004)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  15. Biere, A., Heule, M., van Maaren, H.: Handbook of satisfiability, vol. 185. IOS Press (2009)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  21. Chambers, L.D.: Practical handbook of genetic algorithms: complex coding systems, vol. 3. CRC Press (2010)

    Google Scholar 

  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 

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Correspondence to Vladimir Ulyantsev .

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Ulyantsev, V., Zakirzyanov, I., Shalyto, A. (2015). BFS-Based Symmetry Breaking Predicates for DFA Identification. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham.

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  • Print ISBN: 978-3-319-15578-4

  • Online ISBN: 978-3-319-15579-1

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