Skip to main content

Learning Multiple Languages in Groups

  • Conference paper
Algorithmic Learning Theory (ALT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3734))

Included in the following conference series:

  • 2099 Accesses


We consider a variant of Gold’s learning paradigm where a learner receives as input n different languages (in form of one text where all input languages are interleaved). Our goal is to explore the situation when a more “coarse” classification of input languages is possible, whereas more refined classification is not. More specifically, we answer the following question: under which conditions, a learner, being fed n different languages, can produce m grammars covering all input languages, but cannot produce k grammars covering input languages for any k>m. We also consider a variant of this task, where each of the output grammars may not cover more than r input languages. Our main results indicate that the major factor affecting classification capabilities is the difference nm between the number n of input languages and the number m of output grammars. We also explore relationship between classification capabilities for smaller and larger groups of input languages. For the variant of our model with the upper bound on the number of languages allowed to be represented by one output grammar, for classes consisting of disjoint languages, we found complete picture of relationship between classification capabilities for different parameters n (the number of input languages), m (number of output grammars), and r (bound on the number of languages represented by each output grammar). This picture includes a combinatorial characterization of classification capabilities for the parameters n,m,r of certain types.

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others


  1. Bārzdiņš, J.: Two theorems on the limiting synthesis of functions. In: Theory of Algorithms and Programs, vol. 1, pp. 82–88. Latvian State University (1974) (in Russian)

    Google Scholar 

  2. Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  3. Blum, M.: A machine-independent theory of the complexity of recursive functions. Journal of the ACM 14, 322–336 (1967)

    Article  MATH  Google Scholar 

  4. Case, J., Lynes, C.: Machine inductive inference and language identification. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 107–115. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  5. Case, J., Smith, C.: Comparison of identification criteria for machine inductive inference. Theoretical Computer Science 25, 193–220 (1983)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Jain, S., Ng, Y.K., Tay, T.S.: Learning languages in a union (2005). Preliminary version appeared in ALT (2001)

    Google Scholar 

  8. Machtey, M., Young, P.: An Introduction to the General Theory of Algorithms. North Holland, New York (1978)

    Google Scholar 

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

    Google Scholar 

  10. Osherson, D., Weinstein, S.: Criteria of language learning. Information and Control 52, 123–138 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  11. Pinker, S.: Formal models of language learning. Cognition 7, 217–283 (1979)

    Article  Google Scholar 

  12. Rogers, H.: Gödel numberings of partial recursive functions. Journal of Symbolic Logic 23, 331–341 (1958)

    Article  MathSciNet  Google Scholar 

  13. Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967); Reprinted by MIT Press in 1987

    Google Scholar 

  14. Wexler, K., Culicover, P.: Formal Principles of Language Acquisition. MIT Press, Cambridge (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jain, S., Kinber, E. (2005). Learning Multiple Languages in Groups. In: Jain, S., Simon, H.U., Tomita, E. (eds) Algorithmic Learning Theory. ALT 2005. Lecture Notes in Computer Science(), vol 3734. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29242-5

  • Online ISBN: 978-3-540-31696-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics