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Deleting String Rewriting Systems Preserve Regularity

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Developments in Language Theory (DLT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2710))

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Abstract

A string rewriting system R is called deleting if there exists a partial ordering on its alphabet such that each letter in the right hand side of a rule is less than some letter in the corresponding left hand side. We show that the rewrite relation R* induced by R can be represented as the composition of a finite substitution (into an extended alphabet), a rewrite relation of an inverse context-free system (over the extended alphabet), and a restriction (to the original alphabet). Here, a system is called inverse context-free if |r| ≤ 1 for each rule ℓ → r. The decomposition result directly implies that deleting systems preserve regularity, and that inverse deleting systems preserve context-freeness. The latter result was already obtained by Hibbard [Hib74].

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik/Informatik, Universität Kassel, D-34109, Kassel, Germany

    Dieter Hofbauer

  2. Fakultät für Mathematik und Informatik, Universität Leipzig, D-04109, Leipzig, Germany

    Johannes Waldmann

Authors
  1. Dieter Hofbauer
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  2. Johannes Waldmann
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Szeged, Árpád tér 2, 6720, Szeged, Hungary

    Zoltán Ésik  & Zoltán Fülöp  & 

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Hofbauer, D., Waldmann, J. (2003). Deleting String Rewriting Systems Preserve Regularity. In: Ésik, Z., Fülöp, Z. (eds) Developments in Language Theory. DLT 2003. Lecture Notes in Computer Science, vol 2710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45007-6_27

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  • DOI: https://doi.org/10.1007/3-540-45007-6_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40434-7

  • Online ISBN: 978-3-540-45007-8

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