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Closure of Language Classes Under Bounded Duplication

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Developments in Language Theory (DLT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4036))

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Abstract

Duplication is an operation generating a language from a single word by iterated application of rewriting rules u →uu on factors. We extend this operation to entire languages and investigate, whether the classes of the Chomsky hierarchy are closed under duplication. Here we treat mainly bounded duplication, where the factors duplicated cannot exceed a given length.

While over two letters the regular languages are closed under bounded duplication, over three or more letters they are not, if the length bound is 4 or greater. For 2 they are closed under duplication, the case of 3 remains open. Finally, the class of context-free languages is closed under duplication over alphabets of any size.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Kyoto, 603-8555, Japan

    Masami Ito

  2. Research Group on Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tàrraco 1, 43005, Tarragona, Catalunya, Spain

    Peter Leupold

  3. Tenri University, Tenri, 632-8510, Japan

    Kayoko Shikishima-Tsuji

Authors
  1. Masami Ito
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  2. Peter Leupold
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  3. Kayoko Shikishima-Tsuji
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara

    Oscar H. Ibarra

  2. School of Electrical Engineering and Computer Science, Washington State University, WA 99164, Pullman, USA

    Zhe Dang

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© 2006 Springer-Verlag Berlin Heidelberg

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Ito, M., Leupold, P., Shikishima-Tsuji, K. (2006). Closure of Language Classes Under Bounded Duplication. In: Ibarra, O.H., Dang, Z. (eds) Developments in Language Theory. DLT 2006. Lecture Notes in Computer Science, vol 4036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779148_22

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  • DOI: https://doi.org/10.1007/11779148_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35428-4

  • Online ISBN: 978-3-540-35430-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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