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Efficient Symmetry Breaking for SAT-Based Minimum DFA Inference

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Language and Automata Theory and Applications (LATA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))


Inference of deterministic finite automata (DFA) finds a wide range of important practical applications. In recent years, the use of SAT and SMT solvers for the minimum size DFA inference problem (MinDFA) enabled significant performance improvements. Nevertheless, there are many problems that are simply too difficult to solve to optimality with existing technologies. One fundamental difficulty of the MinDFA problem is the size of the search space. Moreover, another fundamental drawback of these approaches is the encoding size. This paper develops novel compact encodings for Symmetry Breaking of SAT-based approaches to MinDFA. The proposed encodings are shown to perform comparably in practice with the most efficient, but also significantly larger, symmetry breaking encodings.

IZ was supported by RFBR (project 18-37-00425). AM, AI and JMS were supported by FCT grants ABSOLV (PTDC/CCI-COM/28986/2017), FaultLocker (PTDC/CCI-COM/29300/2017), SAFETY (SFRH/BPD/120315/2016), and SAMPLE (CEECIND/04549/2017). VU was supported by the Government of Russia (Grant 08-08).

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  1. 1.

    The encoding size shown is adapted from the results in [20], taking into account that both \(|T^{+}|\) and \(|T^{-}|\) can grow with \(N=|T|\). The size of \(|\varSigma |\) is assumed constant.

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  3. 3.


  1. Abela, J., Coste, F., Spina, S.: Mutually compatible and incompatible merges for the search of the smallest consistent DFA. In: ICGI, pp. 28–39 (2004)

    Chapter  Google Scholar 

  2. Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)

    Article  MathSciNet  Google Scholar 

  3. Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality networks: a theoretical and empirical study. Constraints 16(2), 195–221 (2011)

    Article  MathSciNet  Google Scholar 

  4. Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Commun. 25(2), 97–116 (2012)

    MathSciNet  MATH  Google Scholar 

  5. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)

    Google Scholar 

  6. Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behavior. IEEE Trans. Comput. 21(6), 592–597 (1972)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  8. Coste, F., Nicolas, J.: Regular inference as a graph coloring problem. In: IWGI (1997)

    Google Scholar 

  9. Coste, F., Nicolas, J.: How considering incompatible state mergings may reduce the DFA induction search tree. In: ICGI, pp. 199–210 (1998)

    Google Scholar 

  10. Eén, N., Sörensson, N.: Translating Pseudo-Boolean constraints into SAT. JSAT 2(1–4), 1–26 (2006)

    MATH  Google Scholar 

  11. Gent, I.P., Nightingale, P.: A new encoding of all different into SAT. In: Workshop on Modelling and Reformulating Constraint Satisfaction Problems, pp. 95–110 (2004)

    Google Scholar 

  12. Grinchtein, O., Leucker, M., Piterman, N.: Inferring network invariants automatically. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 483–497. Springer, Heidelberg (2006).

    Chapter  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 (LNAI), vol. 6339, pp. 66–79. Springer, Heidelberg (2010).

    Chapter  Google Scholar 

  14. Heule, M., Verwer, S.: Software model synthesis using satisfiability solvers. Empir. Softw. Eng. 18(4), 825–856 (2013)

    Article  Google Scholar 

  15. de la Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognit. 38(9), 1332–1348 (2005)

    Article  Google Scholar 

  16. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation - International Edition, 2nd edn. Addison-Wesley, Boston (2003)

    MATH  Google Scholar 

  17. Lang, K.J.: Faster algorithms for finding minimal consistent DFAs. Technical report, NEC Research Institute (1999)

    Google Scholar 

  18. 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., Slutzki, G. (eds.) ICGI 1998. LNCS, vol. 1433, pp. 1–12. Springer, Heidelberg (1998).

    Chapter  Google Scholar 

  19. Morgado, A., Heras, F., Liffiton, M.H., Planes, J., Marques-Silva, J.: Iterative and core-guided MaxSAT solving: a survey and assessment. Constraints 18(4), 478–534 (2013)

    Article  MathSciNet  Google Scholar 

  20. Neider, D.: Applications of automata learning in verification and synthesis. Ph.D. thesis, RWTH Aachen University (2014)

    Google Scholar 

  21. Neider, D., Jansen, N.: Regular model checking using solver technologies and automata learning. In: NFM, pp. 16–31 (2013)

    Google Scholar 

  22. Oliveira, A.L., Marques-Silva, J.: Efficient algorithms for the inference of minimum size DFAs. Mach. Learn. 44(1/2), 93–119 (2001)

    Article  Google Scholar 

  23. Sinz, C.: Towards an optimal CNF encoding of Boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005).

    Chapter  MATH  Google Scholar 

  24. Trakhtenbrot, B.A., Barzdin, Y.M.: Finite Automata: Behavior and Synthesis. North-Holland Publishing Company, Amsterdam (1973)

    MATH  Google Scholar 

  25. Ulyantsev, V., Tsarev, F.: Extended finite-state machine induction using SAT-solver. In: ICMLA, pp. 346–349 (2011)

    Google Scholar 

  26. Ulyantsev, V., Zakirzyanov, I., Shalyto, A.: BFS-based symmetry breaking predicates for DFA identification. In: Dediu, A.-H., Formenti, E., Martín-Vide, C., Truthe, B. (eds.) LATA 2015. LNCS, vol. 8977, pp. 611–622. Springer, Cham (2015).

    Chapter  Google Scholar 

  27. Verwer, S., Hammerschmidt, C.A.: flexfringe: a passive automaton learning package. In: ICSME, pp. 638–642 (2017)

    Google Scholar 

  28. Walkinshaw, N., Lambeau, B., Damas, C., Bogdanov, K., Dupont, P.: STAMINA: a competition to encourage the development and assessment of software model inference techniques. Empir. Softw. Eng. 18(4), 791–824 (2013)

    Article  Google Scholar 

  29. Wieman, R., Aniche, M.F., Lobbezoo, W., Verwer, S., van Deursen, A.: An experience report on applying passive learning in a large-scale payment company. In: ICSME, pp. 564–573 (2017)

    Google Scholar 

  30. Zakirzyanov, I., Shalyto, A., Ulyantsev, V.: Finding all minimum-size DFA consistent with given examples: SAT-based approach. In: Cerone, A., Roveri, M. (eds.) SEFM 2017. LNCS, vol. 10729, pp. 117–131. Springer, Cham (2018).

    Chapter  Google Scholar 

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Zakirzyanov, I., Morgado, A., Ignatiev, A., Ulyantsev, V., Marques-Silva, J. (2019). Efficient Symmetry Breaking for SAT-Based Minimum DFA Inference. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham.

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