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International Conference on Algorithmic Learning Theory

ALT 2016: Algorithmic Learning Theory pp 189–203Cite as

Learning Pattern Languages over Groups

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9925))

Abstract

This article studies the learnability of classes of pattern languages over automatic groups. It is shown that the class of bounded unions of pattern languages over finitely generated Abelian automatic groups is explanatorily learnable. For patterns in which variables occur at most n times, it is shown that the classes of languages generated by such patterns as well as their bounded unions are, for finitely generated automatic groups, explanatorily learnable by an automatic learner. In contrast, automatic learners cannot learn the unions of up to two arbitrary pattern languages over the integers. Furthermore, there is an algorithm which, given an automaton describing a group G, generates a learning algorithm \(M_G\) such that either \(M_G\) explanatorily learns all pattern languages over G or there is no learner for this set of languages at all, not even a non-recursive one. For some automatic groups, non-learnability results of natural classes of pattern languages are provided.

S. Jain is supported in part by NUS grants R146-000-181-112, R252-000-534-112 and C252-000-087-001.

F. Stephan is supported in part by NUS grants R146-000-181-112 and R252-000-534-112.

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Acknowledgements

The authors would like to thank the referees for detailed comments that helped to improve the presentation of this article.

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Authors and Affiliations

  1. Institute 1, Faculty of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Rupert Hölzl

  2. School of Computing, National University of Singapore, Singapore, 117417, Republic of Singapore

    Sanjay Jain & Frank Stephan

  3. Department of Mathematics, National University of Singapore, Singapore, 119076, Republic of Singapore

    Frank Stephan

Authors
  1. Rupert Hölzl
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  2. Sanjay Jain
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  3. Frank Stephan
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Corresponding author

Correspondence to Sanjay Jain .

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Editors and Affiliations

  1. Montanuniversität Leoben , Leoben, Austria

    Ronald Ortner

  2. Ruhr-Uni-Bochum , Bochum, Germany

    Hans Ulrich Simon

  3. University of Regina , Regina, Saskatchewan, Canada

    Sandra Zilles

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Hölzl, R., Jain, S., Stephan, F. (2016). Learning Pattern Languages over Groups. In: Ortner, R., Simon, H., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2016. Lecture Notes in Computer Science(), vol 9925. Springer, Cham. https://doi.org/10.1007/978-3-319-46379-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-46379-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46378-0

  • Online ISBN: 978-3-319-46379-7

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