Polynomial time inductive inference of regular term tree languages from positive data

  • Satoshi Matsumoto
  • Yukiko Hayashi
  • Takayoshi Shoudai
Session 7
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1316)


Term graphs are a kind of hypergraphs such that arbitrary graphs can be put to the place of their hyperedges. Each hyperedge in a term graph is labeled with a variable. A term graph is called regular if each variable attached to a hyperedge does not occur more than once. Let f be a regular term graph. If a regular term graph which is obtained from f by substituting any tree becomes also a tree, f is called a regular term tree. We study polynomial time inductive inference of regular term tree languages. This graph language is an extension of pattern languages of strings. We show that some classes of regular term tree languages of term caterpillars are polynomial time inductive inferable.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Angluin. Finding patterns common to a set of strings. Journal of Computer and System Science, 21:46–62, 1980.CrossRefGoogle Scholar
  2. 2.
    D. Angluin. Inductive inference of formal languages from positive data. Information and Control, 45:117–135, 1980.CrossRefGoogle Scholar
  3. 3.
    C. Domingo and J. Shawa-Taylor. The complexity of learning minor closed graph classes. In Proceedings of the 6th Workshop on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence 997, pages 249–260, 1995.Google Scholar
  4. 4.
    M. R. Garey and D. S. Johnson. Computers and Intractability. W.H.Freeman and company, 1983.Google Scholar
  5. 5.
    E. M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967.CrossRefGoogle Scholar
  6. 6.
    J.van.Leeuwen. Graph algorithms. In J.van.Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, chapter 10, pages 525–631. The MIT Press, 1990.Google Scholar
  7. 7.
    I. Koch, T. Lengauer and E. Wanke. An algorithm for finding maximal common subtopologies in a set of protein structure. Journal of Computational Biology, 3:289–306, 1996.PubMedGoogle Scholar
  8. 8.
    A. Marron. Learning pattern languages from a single initial example and from queries. In Proceedings of the first Annual Conference on Computational Learning Theory, pages 311–325, 1988.Google Scholar
  9. 9.
    O. Maruyama and S. Miyano. Graph inference from a walk for trees of bounded degree 3 is NP-complete. In Mathematical Foundations of Computer Science 1995 (Lecture Notes in Computer Science 969), pages 257–266, 1995.Google Scholar
  10. 10.
    S.-Y.Le, R.Nussinov and J.V.Maizel. Tree graphs of RNA secondary structures and their comparisons. Computers and Biomedical Research, 22:461–473, 1989.PubMedGoogle Scholar
  11. 11.
    T. Shinohara. Studies on Inductive Inference from Positive Data. PhD thesis, Kyushu University, 1986.Google Scholar
  12. 12.
    S. Tani and K. Yamazaki. Learning of restricted RNLC graph languages. In Proceedings of the 6th International Symposium Algorithms and Computation, pages 171–180, 1995.Google Scholar
  13. 13.
    T. Uchida. Formal Graph Systems and Parallel Graph Algorithm Design. PhD thesis, Kyushu University, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Satoshi Matsumoto
    • 1
  • Yukiko Hayashi
    • 1
  • Takayoshi Shoudai
    • 1
  1. 1.Department of InformaticsKyushu University 33FukuokaJapan

Personalised recommendations