Skip to main content
SpringerLink
Log in

On Sufficient Conditions to Identify in the Limit Classes of Grammars from Polynomial Time and Data

  • Conference paper
  • First Online:
Grammatical Inference: Algorithms and Applications (ICGI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2484))

Included in the following conference series:

Abstract

Linearity and determinism seem to be two essential conditions for polynomial learning of grammars to be possible. We propose a general condition valid for certain subclasses of the linear grammars given which these classes can be polynomially identified in the limit from given data. This enables us to give new proofs of the identification of well known classes of grammars, and to propose a new (and larger) class of linear grammars for which polynomial identification is thus possible.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Angluin. Learning regular sets from queries and counterexamples. Information and Control, 39:337–350, 1987.

    Article  MathSciNet  Google Scholar 

  2. D. Angluin. Queries revisited. In Proceedings of ALT 2001, pages 12–31. Springer-Verlag, 2001.

    Google Scholar 

  3. A. Brazma, I. Jonassen, J. Vilo, and E. Ukkonen. Pattern discovery in biosequences. In V. Honavar and G. Slutski, editors, Grammatical Inference, ICGI’ 98, number 1433 in LNCS, pages 257–270, Berlin, Heidelberg, 1998. Springer-Verlag.

    Chapter  Google Scholar 

  4. C. de la Higuera. Characteristic sets for polynomial grammatical inference. Machine Learning, 27:125–138, 1997.

    Article  MATH  Google Scholar 

  5. C. de la Higuera and J. Oncina. Learning deterministic linear languages. In R. H. Sloan J. Kivinen, editor, Proceedings of COLT 2002, volume 2375 of LNCS, pages 185–200. Springer-Verlag, 2002.

    Google Scholar 

  6. H. Fernau. Identification of function distinguishable languages. In S. Jain H. Arimura and A. Sharma, editors, Proceedings of the 11th International Conference on Algorithmic Learning Theory (ALT 2000), volume 1968, pages 116–130, Berlin, Heidelberg, 2000. Springer-Verlag.

    Google Scholar 

  7. H. Fernau. Learning XML grammars. In P. Perner, editor, Machine Learning and Data Mining in Pattern Recognition MLDM’01, number 2123, pages 73–87. Springer-Verlag, 2001.

    Google Scholar 

  8. M. Gold. Complexity of automaton identification from given data. Information and Control, 37:302–320, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  9. Lisa Hellerstein, Krishnan Pillaipakkamnatt, Vijay Raghavan, and Dawn Wilkins. How many queries are needed to learn? Journal of the ACM, 43(5):840–862, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Kearns and L. Valiant. Cryptographic limitations on learning boolean formulae and finite automata. In 21st ACM Symposium on Theory of Computing, pages 433–444, 1989.

    Google Scholar 

  11. S. Lee. Learning of context-free languages: A survey of the literature. Technical Report TR-12-96, Center for Research in Computing Technology, Harvard University, Cambridge, Massachusetts, 1996.

    Google Scholar 

  12. K. J. Lang, B. A. Pearlmutter, and R. A. Price. Results of the Abbadingo one DFA learning competition and a new evidence-driven state merging algorithm. In Grammatical Inference, number 1433 in LNCS, pages 1–12. Springer-Verlag, 1998.

    Chapter  Google Scholar 

  13. J. Oncina and P. García. Identifying regular languages in polynomial time. In H. Bunke, editor, Advances in Structural and Syntactic Pattern Recognition, volume 5 of Series in Machine Perception and Artificial Intelligence, pages 99–108. World Scientific, 1992.

    Google Scholar 

  14. L. Pitt. Inductive inference, DFA’s, and computational complexity. In Analogical and Inductive Inference, number 397 in LNCS, pages 18–44. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  15. L. Pitt and M. Warmuth. The minimum consistent DFA problem cannot be approximated within any polynomial. Journal of the Association for Computing Machinery, 40(1):95–142, 1993.

    MATH  MathSciNet  Google Scholar 

  16. Y. Sakakibara. Learning context-free grammars from structural data in polynomial time. Theoretical Computer Science, 76:223–242, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Sakakibara. Recent advances of grammatical inference. Theoretical Computer Science, 185:15–45, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. M. Sempere and P. García. A characterisation of even linear languages and its application to the learning problem. In R. C. Carrasco and J. Oncina, editors, Grammatical Inference and Applications, ICGI-94, number 862 in LNCS, pages 38–44, Berlin, Heidelberg, 1994. Springer

    Google Scholar 

  19. A. Stolcke. An efficient probablistic context-free parsing algorithm that computes prefix probabilities. Linguistics, 21(2):165–201, 1995.

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  21. G. Valiant. A theory of the learnable. Communications of the Association for Computing Machinery, 27(11):1134–1142, 1984.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EURISE, Université de Saint-Etienne, 23 rue du Docteur Paul Michelon, 42023, Saint-Etienne, France

    Colin de la Higuera

  2. Departamento de Lenguajes y Sistemas Informáticos, Universidad de Alicante, Ap.99, E-03080, Alicante, Spain

    Jose Oncina

Authors
  1. Colin de la Higuera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jose Oncina
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Perot Systems Nederland B.V., Hoefseweg 1, 3821 AE, Amersfoort, The Netherlands

    Pieter Adriaans (Senior Research Advisor, Professor of Learning and Adaptive Systems) (Senior Research Advisor, Professor of Learning and Adaptive Systems)

  2. ILLC/Computation and Complexity Theory, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Pieter Adriaans (Senior Research Advisor, Professor of Learning and Adaptive Systems) (Senior Research Advisor, Professor of Learning and Adaptive Systems)

  3. School of Electrical Engineering and Computer Science, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    Henning Fernau

  4. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Henning Fernau

  5. FNWI/ILLC, Cognitive Systems and Information Processing Group, Universiteit van Amsterdam, Room B-5.39, Nieuwe Achtergracht 166, 1018 WV, Amsterdam, The Netherlands

    Menno van Zaanen

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

de la Higuera, C., Oncina, J. (2002). On Sufficient Conditions to Identify in the Limit Classes of Grammars from Polynomial Time and Data. In: Adriaans, P., Fernau, H., van Zaanen, M. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2002. Lecture Notes in Computer Science(), vol 2484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45790-9_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-45790-9_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44239-4

  • Online ISBN: 978-3-540-45790-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation