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Consistent Polynomial Identification in the Limit

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Algorithmic Learning Theory (ALT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1501))

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Abstract

This paper aims to extend well known results about polynomial update-time bounded learning strategies in a recursion theoretic setting.

We generalize the update-time complexity using the approach of Blum’s computational complexity measures.

It will turn out, that consistency is the first natural condition having a narrowing effect for arbitrary update boundaries. We show the existence of arbitrary hard, as well as an infinite chain of harder and harder consistent learnable sets. The complexity gap between consistent und inconsistent strategies solving the same problem can be arbitary large. We prove an exact characterization for polynomial consistent learnability, giving a deeper insight in the problem of hard consistent learnability.

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Author information

Authors and Affiliations

  1. University of Kaiserslautern, Postfach 30 49, D-67653, Kaiserslautern, Germany

    Werner Stein

Authors
  1. Werner Stein
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Editor information

Editors and Affiliations

  1. AG Künstliche Intelligenz - Expertensysteme, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Michael M. Richter

  2. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Carl H. Smith

  3. AG Algorithmischesn Lernen, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Rolf Wiehagen

  4. Graduate School of Information Science and Electrical Engineering Department of Informatics, Kyushu University, Kassuga, 816-8580, Japan

    Thomas Zeugmann

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© 1998 Springer-Verlag Berlin Heidelberg

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Stein, W. (1998). Consistent Polynomial Identification in the Limit. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1998. Lecture Notes in Computer Science(), vol 1501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49730-7_30

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  • DOI: https://doi.org/10.1007/3-540-49730-7_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65013-3

  • Online ISBN: 978-3-540-49730-1

  • eBook Packages: Springer Book Archive

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