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Polynomial-Time Identification of an Extension of Very Simple Grammars from Positive Data

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Book cover Grammatical Inference: Algorithms and Applications (ICGI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4201))

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Abstract

The class of very simple grammars is known to be polynomial-time identifiable in the limit from positive data. This paper introduces an extension of very simple grammars called right-unique simple grammars, and presents an algorithm that identifies right-unique simple grammars in the limit from positive data. The learning algorithm possesses the following three properties. It computes a conjecture in polynomial time in the size of the input data if we regard the cardinality of the alphabet as a constant. It always outputs a grammar which is consistent with the input data. It never changes the conjecture unless the newly provided example contradicts the previous conjecture. The algorithm has a sub-algorithm that solves the inclusion problem for a superclass of right-unique simple grammars, which is also presented in this paper.

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References

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

    Article  MATH  Google Scholar 

  2. Yokomori, T.: Polynomial-time identification of very simple grammars from positive data. Theoretical Computer Science 298, 179–206 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Wakatsuki, M., Teraguchi, K., Tomita, E.: Polynomial time identification of strict deterministic restricted one-counter automata in some class from positive data. In: Paliouras, G., Sakakibara, Y. (eds.) ICGI 2004. LNCS (LNAI), vol. 3264, pp. 260–272. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Linna, M.: Two decidability results for deterministic pushdown automata. Journal of Computer and System Science 18, 92–107 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  5. Greibach, S.A., Friedman, E.P.: Superdeterministic PDAs: A subcase with a decidable inclusion problem. Journal of the Association for Computing Machinery 27(4), 675–700 (1980)

    MATH  MathSciNet  Google Scholar 

  6. Shibata, T., Yoshinaka, R., Chikayama, T.: Probabilistic generalization of simple grammars and its application to reinforcement learning. In: Balcázar, J.L., Long, P.M., Stephan, F. (eds.) ALT 2006. LNCS (LNAI), vol. 4264, pp. 348–362. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Angluin, D.: Inference of reversible languages. Journal of the Association for Computing Machinery 29(3), 741–765 (1982)

    MATH  MathSciNet  Google Scholar 

  8. Wakatsuki, M., Tomita, E.: A fast algorithm for checking the inclusion for very simple deterministic pushdown automata. IEICE transactions on information and systems E76-D(10), 1224–1233 (1993)

    Google Scholar 

  9. Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45(2), 117–135 (1980)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. National Institute of Informatics, University of Tokyo,  

    Ryo Yoshinaka

Authors
  1. Ryo Yoshinaka
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Editor information

Editors and Affiliations

  1. Department of Biosciences and Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, 223-8522, Yokohama, Japan

    Yasubumi Sakakibara

  2. Dept. of Computer Science, Kyoto Sangyo University, Kamigamo Motoyama, Kita-ku, Kyoto, Japan

    Satoshi Kobayashi

  3. Japan Biological Informatics Consortium, 10F TIME24 Building, 2-45 Aomi, Koto-ku, 135-8073, Tokyo, Japan

    Kengo Sato

  4. Department of Information and Communication Engineering, Graduate School of Electro-Communications, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, 182-8585, Tokyo, Japan

    Tetsuro Nishino

  5. Department of Information and Communication Engineering, Faculty of Electro-Communications, The University of Electro-Communications, Chofugaoka 1–5–1, Chofu, 182-8585, Tokyo, Japan

    Etsuji Tomita

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© 2006 Springer-Verlag Berlin Heidelberg

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Yoshinaka, R. (2006). Polynomial-Time Identification of an Extension of Very Simple Grammars from Positive Data. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2006. Lecture Notes in Computer Science(), vol 4201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11872436_5

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  • DOI: https://doi.org/10.1007/11872436_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45264-5

  • Online ISBN: 978-3-540-45265-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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