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Learning k-piecewise testable languages from positive data

  • Session: Algebraic Methods and Algorithms 3
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Grammatical Interference: Learning Syntax from Sentences (ICGI 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1147))

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Abstract

A k-piecewise testable language (k-PWT) is defined by the subwords (sequences of symbols which are not necessarely consecutive) no longer than k that are contained in its words. We propose an algorithm that identifies in the limit the class of k-PWT languages from positive data. The proposed algorithm has polynomial time complexity on the length of the received data. As the class of k-PTW languages is finite, the algorithm can be used for PAC- learning.

Work partially supported by the Spanish CICYT under grant TIC93-0633-CO2

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References

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

    Article  Google Scholar 

  2. Angluin, D. Inference of reversible languages. Journal of the ACM 29 (3). pp. 741–765, 1982.

    Article  Google Scholar 

  3. Anthony, M. and Biggs, N. Computational Learning Theory. An Introduction. Cambridge University Press, 1991.

    Google Scholar 

  4. Biermann A.W. and Feldman, J.A. On the synthesis of finite state machines from samples of their behavior. IEEE Trans. on Computers, Vol. C-21 pp. 592–597, 1972.

    Google Scholar 

  5. Brzozowski, J,A. and Simon, I. Characterizations of Locally Testable Events. Discrete Mathematics, 4. pp. 243–271. 1973.

    Article  Google Scholar 

  6. Pu, K.S. Syntactic Pattern Recognition and Applications. Prentice Hall, 1982.

    Google Scholar 

  7. P.García and E. Vidal. Inference of k-testable Languages in the Strict Sense and application to Syntactic Pattern Recognition. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-12 pp.920–925, 1990.

    Article  Google Scholar 

  8. Gold, E.M. Language identification in the limit. Information and Control, 10. pp. 447–474, 1967.

    Article  Google Scholar 

  9. González R.C. and Thomason, M.G. Syntactic Pattern Recognition: An Introduction. Addison Wesley, 1978.

    Google Scholar 

  10. Knuutila, T. How to invent characterizable methods for regular languages. Lecture Notes in Computer Science 744, Springer Verlag, pp. 209–222, 1993.

    Google Scholar 

  11. Lothaire, M. Combinatorics on words. Addison Wesley,1983.

    Google Scholar 

  12. Muggleton, S. Inductive Acquisition of Expert Knowledge. Addison-Wesley, 1990.

    Google Scholar 

  13. Natarajan, B. Machine Learning: A theoretical aproach. Morgan Kaufmann P. Inc.1991.

    Google Scholar 

  14. Pin, J.E. Variétés de langages formels. Masson, 1984.

    Google Scholar 

  15. Radhakrisnan, V. and Nagaraja, G. Inference of regular grammars via skeletons. IEEE Trans. System, Man, and Cybernetics, SCM-17. pp. 982–992, 1987.

    Google Scholar 

  16. Shyam Kapur and Gianfranco Bilardi Language learning without overgeneralization. Theoretical Computer Science 141, pp. 151–162, 1995.

    Article  Google Scholar 

  17. Simon, I. Piecewise testable events. Lecture Notes in Computer Science, vol. 33, Springer Verlag, pp. 214–222, 1980.

    Google Scholar 

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Laurent Miclet Colin de la Higuera

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© 1996 Springer-Verlag Berlin Heidelberg

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Ruiz, J., García, P. (1996). Learning k-piecewise testable languages from positive data. In: Miclet, L., de la Higuera, C. (eds) Grammatical Interference: Learning Syntax from Sentences. ICGI 1996. Lecture Notes in Computer Science, vol 1147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033355

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  • DOI: https://doi.org/10.1007/BFb0033355

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61778-5

  • Online ISBN: 978-3-540-70678-6

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