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Locality, Reversibility, and Beyond: Learning Languages from Positive Data

  • Tom Head
  • Satoshi Kobayashi
  • Takashi Yokomori
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1501)

Abstract

In algorithmic learning theory fundamental roles are played by the family of languages that are locally testable in the strict sense and by the family of reversible languages. These two families are shown to be the first two members of an infinite sequence of families of regular languages the members of which are learnable in the limit from positive data only. A uniform procedure is given for deciding, for each regular language R and each of our specified families, whether R belongs to the family. The approximation of arbitrary regular languages by languages belonging to these families is discussed. Further, we will give a uniform scheme for learning these families from positive data. Several research problems are also suggested.

Keywords

reversible languages local languages regular languages identification in the limit from positive data approximate learning 

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References

  1. 1.
    D. Angluin, Inductive inference of formal languages from positive data, Information and Control 45 (1980) 117–135.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    D. Angluin, Inference of reversible languages, Journal of the ACM 29 (1982) 741–765.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    E. W. Dijkstra, A note on two problems in connection with graphs, Numerishe Mathematik, 1 (1959) 269–271.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    E. Mark Gold, Language identification in the limit, Information and Control, 10 (1967), 447–474.CrossRefzbMATHGoogle Scholar
  5. 5.
    Head, T, Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors, Bulletin of Mathematical Biology, 49 (1987) 737–759.zbMATHMathSciNetGoogle Scholar
  6. 6.
    T. Head, Splicing representations of strictly locally testable languages, submitted for publication. (1997)Google Scholar
  7. 7.
    T. Head, Splicing languages generated with one-sided context, submitted for publication. (1997)Google Scholar
  8. 8.
    S. Kobayashi and T. Yokomori, Families of non-counting languages and their learnability from positive data, Intern. Journal of Foundations of Computer Science, 7 309–327 (1996).zbMATHCrossRefGoogle Scholar
  9. 9.
    S. Kobayashi and T. Yokomori, Learning approximately regular languages with reversible languages, Theoretical Computer Science, 174 (1997) 251–257.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    De Luca, A. and A. Restivo, A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup, Information and Control, 44 (1980) 300–319.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    R. McNaughton and S. Papert, Counter-Free Automata, MIT Press, Cambridge, Massachusetts (1971).zbMATHGoogle Scholar
  12. 12.
    M. P. Schutzenberger, Sur certaines operations de fermeture dans les languages rationnels, Symposium Mathematicum, 15 (1975) 245–253.MathSciNetGoogle Scholar
  13. 13.
    T. Yokomori, N. Ishida, and S. Kobayashi, Learning local languages and its application to protein alpha-chain identification, In Proc. of 27th Hawaii Intern. Conf. on System Sciences, IEEE Press, 113–122 (1994).Google Scholar
  14. 14.
    T. Yokomori, On polynomial-time learnability in the limit of strictly deterministic automata, Machine Learning, 19 (1995) 153–179.zbMATHGoogle Scholar
  15. 15.
    T. Yokomori and S. Kobayashi, Learning local languages and its application to DNA sequence analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Tom Head
    • 1
  • Satoshi Kobayashi
    • 2
  • Takashi Yokomori
    • 3
  1. 1.Department of MathematicsBinghamton UniversityBinghamtonUSA
  2. 2.Department of Information ScienceTokyo Denki UniversitySaitamaJapan
  3. 3.Department of Mathematics, School of EducationWaseda UniversityTokyoJapan

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