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Iterative Learning of Simple External Contextual Languages

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Algorithmic Learning Theory (ALT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5254))

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Abstract

It is investigated for which choice of a parameter q, denoting the number of contexts, the class of simple external contextual languages is iteratively learnable. On one hand, the class admits, for all values of q, polynomial time learnability provided an adequate choice of the hypothesis space is given. On the other hand, additional constraints like consistency and conservativeness or the use of a one-one hypothesis space changes the picture — iterative learning limits the long term memory of the learner to the current hypothesis and these constraints further hinder storage of information via padding of this hypothesis. It is shown that if q > 3, then simple external contextual languages are not iteratively learnable using a class preserving one-one hypothesis space, while for q = 1 it is iteratively learnable, even in polynomial time. For the intermediate levels, there is some indication that iterative learnability using a class preserving one-one hypothesis space might depend on the size of the alphabet. It is also investigated for which choice of the parameters, the simple external contextual languages can be learnt by a consistent and conservative iterative learner.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Yale University, New Haven, CT 06520-8285, USA

    Leonor Becerra-Bonache

  2. Department of Computer and Information Sciences, University of Delaware, Newark, DE 19716-2586, USA

    John Case

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

    Sanjay Jain

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

    Frank Stephan

Authors
  1. Leonor Becerra-Bonache
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  2. John Case
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  3. Sanjay Jain
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  4. Frank Stephan
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Editor information

Editors and Affiliations

  1. Computer Science and Engineering, University of California, San Diego, USA

    Yoav Freund

  2. Department of Computer Science and Information Theory, Department of Computer Science and Budapest University of Technology and Economics, Stoczek u. 2, 1521, Budapest, Hungary

    László Györfi

  3. Department of Math., Stat. and Comp. Sci,, University of Illinois, 851 S. Morgan, IL 60607-7045, Chicago, USA

    György Turán

  4. Division of Computer Science, Hokkaido University, N-14, W-9, 060-0814, Sapporo, Japan

    Thomas Zeugmann

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Becerra-Bonache, L., Case, J., Jain, S., Stephan, F. (2008). Iterative Learning of Simple External Contextual Languages. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2008. Lecture Notes in Computer Science(), vol 5254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87987-9_30

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  • DOI: https://doi.org/10.1007/978-3-540-87987-9_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87986-2

  • Online ISBN: 978-3-540-87987-9

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