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Iterated Transductions and Efficient Learning from Positive Data: A Unifying View

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1891))

Abstract

In this paper, we will not focus on a learnability result of some specific language class, but on giving a set of language classes each of which is efficiently learnable in the limit from positive data. Furthermore, the set contains the class of k-reversible languages and the class of k-locally testable languages in the strict sense just as example language classes. This paper also proposes a framework for defining language classes based on iterated transductions. We believe that the framework is quite adequate for theoretically investigate the classes of languages which are efficiently learnable from positive data.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Angluin, D.: Inference of reversible languages. Journal of the ACM 29, 741–765 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arikawa, S., Shinohara, T., Yamamoto, A.: Learning Elementary Formal Systems. Theoretical Computer Science 95, 97–113 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. García, P., Vidal, E.: Inference of k-Testable Languages in the Strict Sense and Application to Syntactic Pattern Recognition. IEEE Trans. on Pattern Analysis and Machine Intelligence 12, 920–925 (1990)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bulletin of Mathematical Biology 49, 737–759 (1987)

    MATH  MathSciNet  Google Scholar 

  7. Head, T., Kobayashi, S., Yokomori, T.: Locality, Reversibility, and Beyond: Learning Languages from Positive Data. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds.) ALT 1998. LNCS (LNAI), vol. 1501, pp. 191–204. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Kobayashi, S.: Approximate Identification, Finite Elasticity and Lattice Structure of Hypothesis Space, Technical Report, CSIM 96-04, Dept. of Compt. Sci. and Inform. Math., Univ. of Electro-Communications (1996)

    Google Scholar 

  9. Kobayashi, S., Mitrana, V., Păun, G., Rozenberg, G.: Formal Properties of PA-Matching. Theoretical Computer Science (accepted for publication)

    Google Scholar 

  10. Kobayashi, S., Yokomori, T.: Learning Approximately Regular Languages with Reversible Languages. Theoretical Computer Science 174, 251–257 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Koshiba, T., Mäkinen, E., Takada, Y.: Learning Strongly Deterministic Even Linear Languages from Positive Examples. In: Zeugmann, T., Shinohara, T., Jantke, K.P. (eds.) ALT 1995. LNCS (LNAI), vol. 997, pp. 41–54. Springer, Heidelberg (1995)

    Google Scholar 

  12. De Luca, A., Restivo, A.: A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup. Information and Control 44, 300–319 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  13. Manca, V., Martín-Vide, C., Păn, G.: Iterated GSM Mappings: A Collapsing Hierarchy, Turku Centre for Computer Science, Technical Report No. 206 (October 1998)

    Google Scholar 

  14. McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)

    MATH  Google Scholar 

  15. Pitt, L.: Inductive Inference, DFAs, and Computational Complexity. In: Jantke, K.P. (ed.) AII 1989. LNCS (LNAI), vol. 397, pp. 18–44. Springer, Heidelberg (1989)

    Google Scholar 

  16. Pixton, D.: Regularity of splicing languages. Discrete Applied Mathematics 69, 101–124 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  17. Schutzenberger, M.P.: Sur certaines operations de fermeture dans les languages rationnels. In: Symposium Mathematicum, vol. 15, pp. 245–253 (1975)

    Google Scholar 

  18. Shinohara, T.: Polynomial-time Inference of Extended Regular Pattern Languages. In: Goto, E., Nakajima, R., Yonezawa, A., Nakata, I., Furukawa, K. (eds.) RIMS 1982. LNCS, vol. 147, pp. 115–127. Springer, Heidelberg (1983)

    Google Scholar 

  19. Shinohara, T.: Rich Classes Inferable from Positive Data: Length Bounded Elementary Formal Systems. Information and Computation 108, 175–186 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  20. Smullyan, R.M.: Theory of Formal Systems. Annals of Mathematics Studies, revised edn., vol. 47, Princeton University Press, Princeton (1961)

    Google Scholar 

  21. Wood, D.: Iterated a-NGSM Maps and Γ Systems. Information and Control 32, 1–26 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  22. Yokomori, T., Ishida, N., Kobayashi, S.: Learning local languages and its application to protein alpha-chain identification. In: Proc. of 27th Hawaii Intern. Conf. on System Sciences, pp. 113–122. IEEE Press, Los Alamitos (1994)

    Google Scholar 

  23. Yokomori, T.: On polynomial-time learnability in the limit of strictly deterministic automata. Machine Learning 19, 153–179 (1995)

    MATH  Google Scholar 

  24. Yokomori, T., Kobayashi, S.: Learning local languages and its application to DNA sequence analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(10), 1067–1079 (1998)

    Article  Google Scholar 

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Kobayashi, S. (2000). Iterated Transductions and Efficient Learning from Positive Data: A Unifying View. In: Oliveira, A.L. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2000. Lecture Notes in Computer Science(), vol 1891. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45257-7_13

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  • DOI: https://doi.org/10.1007/978-3-540-45257-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41011-9

  • Online ISBN: 978-3-540-45257-7

  • eBook Packages: Springer Book Archive

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