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CGE: A Sequential Learning Algorithm for Mealy Automata

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Grammatical Inference: Theoretical Results and Applications (ICGI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6339))

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Abstract

We introduce a new algorithm for sequential learning of Mealy automata by congruence generator extension (CGE). Our approach makes use of techniques from term rewriting theory and universal algebra for compactly representing and manipulating automata using finite congruence generator sets represented as string rewriting systems (SRS). We prove that the CGE algorithm correctly learns in the limit.

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References

  1. Balcazar, J.L., Diaz, J., Gavalda, R.: Algorithms for learning finite automata from queries: a unified view. In: Advances in Algorithms, Languages and Complexity, pp. 53–72. Kluwer, Dordrecht (1997)

    Google Scholar 

  2. Bohlin, T., Jonsson, B.: Regular Inference for Communication Protocol Entities, Tech. Report 2008-024, Dept. of Information Technology, Uppsala University (2008)

    Google Scholar 

  3. Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. North Holland, Amsterdam (1990)

    Google Scholar 

  4. Incremental regular inference. In: Miclet, L., de la Higuera, C. (eds.) ICGI 1996. LNCS(LNAI), vol. 1147, pp. 222–237. Springer, Heidelberg (1996)

    Google Scholar 

  5. What is the search space of the regular inference? In: Carrasco, R.C., Oncina, J. (eds.) ICGI 1994. LNCS, vol. 862, pp. 25–37. Springer, Heidelberg (1994)

    Google Scholar 

  6. Gold, E.M.: Language identification in the limit. Information and Control 10(5), 447–474 (1967)

    Article  MATH  Google Scholar 

  7. Groce, A., Peled, D., Yannakakis, M.: Adaptive Model Checking. Logic Journal of the IGPL 14(5), 729–744 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Knuth, D.E., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–269. Pergamon Press, Oxford (1970)

    Google Scholar 

  9. Lang, K.J.: Random DFA’s can be approximately learned from sparse uniform examples. In: Proc. of 5th ACM workshop on Computational Learning Theory, pp. 45–52 (1992)

    Google Scholar 

  10. Meinke, K.: Automated Black-Box Testing of Functional Correctness using Function Approximation. In: Rothermel, G. (ed.) Proc. ACM SIGSOFT Int. Symp. on Software Testing and Analysis, ISSTA 2004. Software Engineering Notes, vol. 29 (4), pp. 143–153. ACM Press, New York (2004)

    Chapter  Google Scholar 

  11. Meinke, K., Sindhu, M.: On the Correctness and Performance of the IID Incremental Learning Algorithm for DFA, technical report, School of Computer Science and Communication, Royal Institute of Technology, Stockholm (2010)

    Google Scholar 

  12. Meinke, K., Tucker, J.V.: Universal Algebra. In: Abramsky, S., Gabbay, D., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 1, pp. 189–411. Oxford University Press, Oxford (1993)

    Google Scholar 

  13. Oncina, J., Garcia, P.: Inferring regular languages in polynomial update time. In: Perez de la Blanca, N., Sanfeliu, A., Vidal, E. (eds.) Pattern Recognition and Image Analysis. Series in Machine Perception and Artificial Intelligence, vol. 1, pp. 49–61. World Scientific, Singapore (1992)

    Chapter  Google Scholar 

  14. Parekh, R., Honavar, V.: Grammar inference, automata induction and language acquisition. In: Dale, Moisl, Somers (eds.) Handbook of Natural Language Processing. Marcel Dekker, New York

    Google Scholar 

  15. A solution of the syntactic induction-inference problem for regular languages. Computer languages 3, 53–64 (1978)

    Google Scholar 

  16. Parkeh, R.G., Nichitiu, C., Honavar, V.G.: A polynomial time incremental algorithm for regular grammar inference. In: Honavar, V.G., Slutzki, G. (eds.) ICGI 1998. LNCS (LNAI), vol. 1433, p. 37. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  17. Peled, D., Vardi, M.Y., Yannakakis, M.: Black-box Checking. In: Wu, J., et al. (eds.) Formal Methods for Protocol Engineering and Distributed Systems, FORTE/PSTV, Beijing, pp. 225–240. Kluwer, Dordrecht (1999)

    Google Scholar 

  18. Porat, S., Feldman, J.: Learning automata from ordered examples. Machine Learning 7, 109–138 (1991)

    MATH  Google Scholar 

  19. Raffelt, H., Steffen, B., Margaria, T.: Dynamic Testing Via Automata Learning. In: Yorav, K. (ed.) HVC 2007. LNCS, vol. 4899, pp. 136–152. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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Meinke, K. (2010). CGE: A Sequential Learning Algorithm for Mealy Automata. In: Sempere, J.M., García, P. (eds) Grammatical Inference: Theoretical Results and Applications. ICGI 2010. Lecture Notes in Computer Science(), vol 6339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15488-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-15488-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15487-4

  • Online ISBN: 978-3-642-15488-1

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