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Learning in Friedberg Numberings

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Algorithmic Learning Theory (ALT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4754))

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Abstract

In this paper we consider learnability in some special numberings, such as Friedberg numberings, which contain all the recursively enumerable languages, but have simpler grammar equivalence problem compared to acceptable numberings. We show that every explanatorily learnable class can be learnt in some Friedberg numbering. However, such a result does not hold for behaviourally correct learning or finite learning. One can also show that some Friedberg numberings are so restrictive that all classes which can be explanatorily learnt in such Friedberg numberings have only finitely many infinite languages. We also study similar questions for several properties of learners such as consistency, conservativeness, prudence, iterativeness and non U-shaped learning. Besides Friedberg numberings, we also consider the above problems for programming systems with K-recursive grammar equivalence problem.

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Author information

Authors and Affiliations

  1. Department of Computer Science, National University of Singapore, Singapore 117590, Republic of Singapore

    Sanjay Jain

  2. Department of Computer Science and Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore

    Frank Stephan

Authors
  1. Sanjay Jain
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  2. Frank Stephan
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Editor information

Editors and Affiliations

  1. RSISE @ ANU and SML @ NICTA, Canberra,, ACT, 0200, Australia

    Marcus Hutter

  2. Columbia University, NY, P.O. Box, New York, USA

    Rocco A. Servedio

  3. Graduate School of Information Sciences, Tohoku University,, Sendai 980-8579, Japan

    Eiji Takimoto

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© 2007 Springer-Verlag Berlin Heidelberg

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Jain, S., Stephan, F. (2007). Learning in Friedberg Numberings. In: Hutter, M., Servedio, R.A., Takimoto, E. (eds) Algorithmic Learning Theory. ALT 2007. Lecture Notes in Computer Science(), vol 4754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75225-7_10

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  • DOI: https://doi.org/10.1007/978-3-540-75225-7_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75224-0

  • Online ISBN: 978-3-540-75225-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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