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Learning Languages in a Union

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Book cover Algorithmic Learning Theory (ALT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2225))

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Abstract

In inductive inference,a machine is given words in a language and the machine is said to identify the language if it correctly names the language. In this paper we study classes of languages where the unions of up to a fixed number (n say) of languages from the class are identifiable. We distinguish between two different scenarios: in one scenario,the learner need only to name the language which results from the union; in the other, the learner must individually name the languages which make up the union (we say that the unioned language is discerningly identified). We define three kinds of identification criteria based on this and by the use of some naturally occurring classes of languages,demonstrate that the inferring power of each of these identification criterion decreases as we increase the number of languages allowed in the union, thus resulting in an infinite hierarchy for each identification criterion. A comparison between the different identification criteria also yielded similar hierarchies. We show that for each n,there exists a class of disjoint languages where all unions of up to n languages from this class can be discerningly identified,but there is no learner which identifies every union of n+1 languages from this class. We give sufficient conditions for classes of languages where the unions can be discerningly identified. We also present language classes which are complete with respect to weak reduction (in terms of intrinsic complexity) for our identification criteria.

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References

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. H.S.M. Coxeter. Regular Polytopes (2nd ed.). Methuen & Co. Ltd.,London, 1963.

    Google Scholar 

  4. R. Freivalds, E. Kinber,and C. Smith. On the intrinsic complexity of learning. Information and Computation,123(1):64–71,1995.

    Article  MathSciNet  Google Scholar 

  5. S. Goldman and S. Kwek. On learning unions of pattern languages and tree patterns. Algorithmic Learning Theory:T enth International Conference (ALT’ 99),1720:347–363,1999.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. S. Jain and E. Kinber. On intrinsic complexity of learning geometrical concepts from texts. In Proceedings of the Fourteenth Annual Conference on Computational Learning Theory,2001. To appear.

    Google Scholar 

  8. S. Jain, E. Kinber,and R. Wiehagen. Language learning from texts: Degrees of intrinsic complexity and their characterizations. In Nicolo Cesa-Bianchi and Sally Goldman,editors, Proceedings of the Thirteenth Annual Conference on Computational Learning Theory,pages 47–58. Morgan Kaufmann,2000.

    Google Scholar 

  9. S. Jain and A. Sharma. The intrinsic complexity of language identification. Journal of Computer and System Sciences,52:393–402,1996.

    Article  MathSciNet  Google Scholar 

  10. E. Kinber, C. Papazian, C. Smith,and R. Wiehagen. On the intrinsic complexity of learning recursive functions. In Proceedings of the Twelfth Annual Conference on Computational Learning Theory,pages 257–266. ACM Press,1999.

    Google Scholar 

  11. T. Motoki, T. Shinohara,and K. Wright. The correct definition of finite elasticity: Corrigendum to identification of unions. In L. Valiant and M. Warmuth,editors, Proceedings of the Fourth Annual Workshop on Computational Learning Theory,page 375. Morgan Kaufmann,1991.

    Google Scholar 

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

    Google Scholar 

  13. H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw-Hill,1967. Reprinted by MIT Press in 1987.

    Google Scholar 

  14. T. Shinohara and H. Arimura. Inductive inference of unbounded unions of pattern languages from positive data. Theoretical Computer Science A, 241:191–209,2000. Special Issue for ALT’96.

    Article  MathSciNet  Google Scholar 

  15. K. Wright. Identification of unions of languages drawn from an identifiable class. In R. Rivest, D. Haussler,and M. Warmuth,editors, Proceedings of the Second Annual Workshop on Computational Learning Theory,pages 328–333. Morgan Kaufmann,1989.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computing, National University of Singapore, 119260, Singapore

    Sanjay Jain

  2. School of Computing, National University of Singapore, 119260, Singapore

    Yen Kaow Ng

  3. Department of Mathematics, National University of Singapore, 119260, Singapore

    Tiong Seng Tay

Authors
  1. Sanjay Jain
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  2. Yen Kaow Ng
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  3. Tiong Seng Tay
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Editor information

Editors and Affiliations

  1. IBM, Thomas J.Watson Research Center, Room 33-237, P.O.Box 218, 10598, Yorktown, NY, USA

    Naoki Abe

  2. Dept.of Electrical Engineering and Computer Science, Tufts University, 161 College Ave., 02155, Medford, MA, USA

    Roni Khardon

  3. Medizinische Universität zu Lübeck,Inst.für Theoretische Informatik, Wallstr.40, 23560, Lübeck, Germany

    Thomas Zeugmann

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© 2001 Springer-Verlag Berlin Heidelberg

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Jain, S., Ng, Y.K., Tay, T.S. (2001). Learning Languages in a Union. In: Abe, N., Khardon, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2001. Lecture Notes in Computer Science(), vol 2225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45583-3_19

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  • DOI: https://doi.org/10.1007/3-540-45583-3_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42875-6

  • Online ISBN: 978-3-540-45583-7

  • eBook Packages: Springer Book Archive

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