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Learnability of Enumerable Classes of Recursive Functions from “Typical” Examples

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Algorithmic Learning Theory (ALT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1720))

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Abstract

The paper investigates whether it is possible to learn every enumerable classes of recursive functions from “typical” examples. “Typical” means, there is a computable family of finite sets, such that for each function in the class there is one set of examples that can be used in any suitable hypothesis space for this class of functions. As it will turn out, there are enumerable classes of recursive functions that are not learnable from “typical” examples. The learnable classes are characterized.

The results are proved within an abstract model of learning from examples, introduced by Freivalds, Kinber and Wiehagen. Finally, the results are interpreted and possible connections of this theoretical work to the situation in real life classrooms are pointed out.

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References

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Author information

Authors and Affiliations

  1. University of Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Jochen Nessel

Authors
  1. Jochen Nessel
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Editor information

Editors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, 152-8552, Japan

    Osamu Watanabe

  2. Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Takashi Yokomori

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© 1999 Springer-Verlag Berlin Heidelberg

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Nessel, J. (1999). Learnability of Enumerable Classes of Recursive Functions from “Typical” Examples. In: Watanabe, O., Yokomori, T. (eds) Algorithmic Learning Theory. ALT 1999. Lecture Notes in Computer Science(), vol 1720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46769-6_22

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  • DOI: https://doi.org/10.1007/3-540-46769-6_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66748-3

  • Online ISBN: 978-3-540-46769-4

  • eBook Packages: Springer Book Archive

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