Skip to main content

On the Complexity of Consistent Identification of Some Classes of Structure Languages

  • Conference paper

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

Abstract

In [5,7] ‘discovery procedures’ for CCGs were defined that accept a sequence of structures as input and yield a set of grammars.

In [11] it was shown that some of the classes based on these procedures are learnable. The complexity of learning them was still left open.

In this paper it is shown that learning some of these classes is NP-hard under certain restrictions.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angluin, D.: Finding common patterns to a set of strings. In: Proceedings of the 11th Annual Symposium on Theory of Computing, pp. 130–141 (1979)

    Google Scholar 

  2. Angluin, D.: Finding patterns common to a set of strings. Journal of Computer System Sciences 21, 46–62 (1980)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Barzdin, J.: Inductive inference of automata, functions and programs. In: Proceedings International Congress of Math., Vancouver, pp. 455–460 (1974)

    Google Scholar 

  5. Buszkowski, W.: Discovery procedures for categorial grammars. In: Klein, E., van Benthem, J. (eds.) Categories, Polymorphism and Unification, University of Amsterdam (1987)

    Google Scholar 

  6. Buszkowski, W.: Solvable problems for classical categorial grammars. Bulletin of the Polish Academy of Sciences: Mathematics 34, 373–382 (1987)

    MathSciNet  Google Scholar 

  7. Buszkowski, W., Penn, G.: Categorial grammars determined from linguistic data by unification. Studia Logica 49, 431–454 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Daley, R., Smith, C.: On the complexity of inductive inference. Information and Control 69, 12–40 (1986)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. The MIT Press, Cambridge (1999)

    Google Scholar 

  11. Kanazawa, M.: Learnable Classes of Categorial Grammars. CSLI Publications, Stanford University (1998)

    MATH  Google Scholar 

  12. Kearns, M.J., Vazirani, U.V.: An Introduction to Computational Learning Theory. MIT Press, Cambridge (1994)

    Google Scholar 

  13. Matsumoto, S., Hayashi, Y., Shoudai, T.: Polynomial time inductive inference of regular term tree languages from positive data. In: Li, M. (ed.) ALT 1997. LNCS, vol. 1316, pp. 212–227. Springer, Heidelberg (1997)

    Google Scholar 

  14. Motoki, T., Shinohara, T., Wright, K.: The correct definition of finite elasticity: Corrigendum to identification of unions. In: The Fourth Workshop on Computa- tional Learning Theory. Morgan Kaufmann, San Mateo (1991)

    Google Scholar 

  15. Osherson, D.N., de Jongh, D., Martin, E., Weinstein, S.: Formal learning theory. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language. Elsevier Science Publishers, Amsterdam (1996)

    Google Scholar 

  16. Osherson, D.N., Stob, M., Weinstein, S.: Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)

    Google Scholar 

  17. Pitt, L.: Inductive inference, dfas, and computational complexity. In: Jantke, K.P. (ed.) AII 1989. LNCS, vol. 397, pp. 18–44. Springer, Heidelberg (1989)

    Google Scholar 

  18. Shinohara, T.: Studies on Inductive Inference from Positive Data. PhD thesis, Kyushu University (1986)

    Google Scholar 

  19. Stein, W.: Consistent polynominal identification in the limit. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds.) ALT 1998. LNCS (LNAI), vol. 1501, pp. 424–438. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Wiehagen, R., Zeugmann, T.: Learning and consistency. In: Lange, S., Jantke, K.P. (eds.) GOSLER 1994. LNCS, vol. 961, pp. 1–24. Springer, Heidelberg (1995)

    Google Scholar 

  21. Wright, K.: Identification of unions of languages drawn from an identifiable class. In: The 1989 Workshop on Computational Learning Theory, pp. 328–333. Morgan Kaufmann, San Mateo (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Costa Florêncio, C. (2000). On the Complexity of Consistent Identification of Some Classes of Structure Languages. 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_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45257-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41011-9

  • Online ISBN: 978-3-540-45257-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics