Skip to main content
SpringerLink
Log in
Book cover

International Colloquium on Grammatical Inference

ICGI 2010: Grammatical Inference: Theoretical Results and Applications pp 24–37Cite as

Distributional Learning of Some Context-Free Languages with a Minimally Adequate Teacher

  • Conference paper

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

Abstract

Angluin showed that the class of regular languages could be learned from a Minimally Adequate Teacher (mat) providing membership and equivalence queries. Clark and Eyraud (2007) showed that some context free grammars can be identified in the limit from positive data alone by identifying the congruence classes of the language. In this paper we consider learnability of context free languages using a mat. We show that there is a natural class of context free languages, that includes the class of regular languages, that can be polynomially learned from a mat, using an algorithm that is an extension of Angluin’s lstar algorithm.

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

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. Clark, A., Eyraud, R.: Polynomial identification in the limit of substitutable context-free languages. Journal of Machine Learning Research 8, 1725–1745 (2007)

    MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  3. Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75(2), 87–106 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. Clark, A., Eyraud, R., Habrard, A.: A polynomial algorithm for the inference of context free languages. In: Clark, A., Coste, F., Miclet, L. (eds.) ICGI 2008. LNCS (LNAI), vol. 5278, pp. 29–42. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Shirakawa, H., Yokomori, T.: Polynomial-time MAT Learning of C-Deterministic Context-free Grammars. Transactions of the information processing society of Japan 34, 380–390 (1993)

    Google Scholar 

  6. Boasson, L., Sénizergues, S.: NTS languages are deterministic and congruential. J. Comput. Syst. Sci. 31(3), 332–342 (1985)

    Article  MATH  Google Scholar 

  7. Ginsburg, S.: The Mathematical Theory of Context-Free Languages. McGraw-Hill, Inc., New York (1966)

    MATH  Google Scholar 

  8. Takada, Y.: Grammatical inference for even linear languages based on control sets. Information Processing Letters 28(4), 193–199 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Yoshinaka, R.: Identification in the Limit of k-l-Substitutable Context-Free Languages. In: Clark, A., Coste, F., Miclet, L. (eds.) ICGI 2008. LNCS (LNAI), vol. 5278, pp. 266–279. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Gold, E.M.: Complexity of automaton identification from given data. Information and Control 37(3), 302–320 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  11. Angluin, D.: Negative results for equivalence queries. Machine Learning 5(2), 121–150 (1990)

    Google Scholar 

  12. Combe, D., de la Higuera, C., Janodet, J.C.: Zulu: an interactive learning competition. In: Yli-Jyrä, A. (ed.) FSMNLP 2009. LNCS(LNAI), vol. 6062, pp. 139–146. Springer, Heidelberg (2010)

    Google Scholar 

  13. Sénizergues, G.: The equivalence and inclusion problems for NTS languages. J. Comput. Syst. Sci. 31(3), 303–331 (1985)

    Article  MATH  Google Scholar 

  14. Engelfriet, J.: Deciding the NTS property of context-free grammars. Results and Trends in Theoretical Computer Science, 124–130 (1994)

    Google Scholar 

  15. Gore, V., Jerrum, M., Kannan, S., Sweedyk, Z., Mahaney, S.: A Quasi-polynomial-time Algorithm for Sampling Words from a Context-Free Language. Information and Computation 134(1), 59–74 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Starkie, B., van Zaanen, M., Estival, D.: The Tenjinno Machine Translation Competition. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds.) ICGI 2006. LNCS (LNAI), vol. 4201, pp. 214–226. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Starkie, B., Coste, F., van Zaanen, M.: The Omphalos context-free grammar learning competition. In: Paliouras, G., Sakakibara, Y. (eds.) ICGI 2004. LNCS (LNAI), vol. 3264, pp. 16–27. Springer, Heidelberg (2004)

    Google Scholar 

  18. de la Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognition 38(9), 1332–1348 (2005)

    Article  Google Scholar 

  19. Clark, A.: A learnable representation for syntax using residuated lattices. In: Proceedings of the 14th Conference on Formal Grammar, Bordeaux, France (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London,  

    Alexander Clark

Authors
  1. Alexander Clark
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Sistemas Informáticos y Computatión, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

    José M. Sempere  & Pedro García  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Clark, A. (2010). Distributional Learning of Some Context-Free Languages with a Minimally Adequate Teacher. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15488-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15487-4

  • Online ISBN: 978-3-642-15488-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation