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Inferring a system from examples with time passage

  • Yasuhito Mukouchi
Session 7
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1316)

Abstract

We consider inferring a system from examples with time passage, which we will call an observation. A complete observation is a possibly infinite sequence (p0, p1,...,pn, ...) of examples, where the (n+1)-st example pn of the sequence is chosen nondeterministically from possible candidates that may depend on the time n and the former examples p0,p1 ... , pn-1. We call the set of all possible complete observations a phenomenon. A phenomenon we introduce is turned out to be a generalization of a formal language as well as a function.

We propose a system that generates a phenomenon and discuss inferability in the limit, finite inferability and refutable inferability of systems from their observations. First, we give some characterization theorems on inferability. We also consider inferability from presentations with some additional informations. Finally, we propose phenomena generated by finite automata and discuss their inferability.

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References

  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data, Information and Control 45 (1980) 117–135.CrossRefGoogle Scholar
  2. 2.
    Gold, E.M.: Language identification in the limit, Information and Control 10 (1967) 447–474.CrossRefGoogle Scholar
  3. 3.
    Hopcroft, J.E. and Ullman, J.D.: “Introduction to automata theory, languages and computation,” Addison-Wesley Co. Inc. Reading, 1979.Google Scholar
  4. 4.
    Kapur, S.: Computational learning of languages, PhD thesis, Technical Report 91-1234, Cornell University, 1991.Google Scholar
  5. 5.
    Kapur, S.: Monotonic language learning, in Proceedings of the 3rd Workshop on Algorithmic Learning Theory (1992), Lecture Notes in Artificial Intelligence 743 (1993) 147–158.Google Scholar
  6. 6.
    Lange, S. and Zeugmann, T.: Types of monotonic language learning and their characterization, in Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory (1992) 377–390.Google Scholar
  7. 7.
    Motoki, T, Shinohara, T. and Wright, K.: The correct definition of finite elasticity: corrigendum to identification of unions, in Proceedings of the 4th Annual ACM Workshop on Computational Learning Theory (1991) 375–375.Google Scholar
  8. 8.
    Mukouchi, Y.: Characterization of finite identification, in Proceedings of the 3rd International Workshop on Analogical and Inductive Inference, Lecture Notes in Artificial Intelligence 642 (1992) 260–267.Google Scholar
  9. 9.
    Mukouchi, Y. and Arikawa, S.: Inductive inference machines that can refute hypothesis spaces, in Proceedings of the 4th International Workshop on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence 744 (1993) 123–137.Google Scholar
  10. 10.
    Mukouchi, Y. and Arikawa, S.: Towards a mathematical theory of machine discovery from facts, Theoretical Computer Science 137 (1995) 53–84.Google Scholar
  11. 11.
    Sato, M. and Moriyama, T.: Inductive inference of length-bounded EFS's from positive data, DMIS Research Report 94-2, Osaka Prefecture University, 1994.Google Scholar
  12. 12.
    Sato, M. and Umayahara, K.: Inductive inferability for formal languages from positive data, in Proceedings of the 2nd Workshop on Algorithmic Learning Theory (1991) 84–92 (also in IEICE Trans. Inf. & Syst. E75-D No. 4 (1992) 415–419).Google Scholar
  13. 13.
    Wright, K.: Identification of unions of languages drawn from an identifiable class, in Proceedings of the 2nd Annual Workshop on Computational Learning Theory (1989) 328–333Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Yasuhito Mukouchi
    • 1
  1. 1.Department of Mathematics and Information SciencesCollege of Integrated Arts and SciencesSakai, OsakaJapan

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