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Match-Bounded String Rewriting Systems

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Mathematical Foundations of Computer Science 2003 (MFCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2747))

Abstract

We investigate rewriting systems on strings by annotating letters with natural numbers, so called match heights. A position in a reduct will get height h+1 if the minimal height of all positions in the redex is h. In a match-bounded system, match heights are globally bounded. Exploiting recent results on deleting systems, we prove that it is decidable whether a given rewriting system has a given match bound. Further, we show that match-bounded systems preserve regularity of languages. Our main focus, however, is on termination of rewriting. Match-bounded systems are shown to be linearly terminating, and–more interestingly–for inverses of match-bounded systems, termination is decidable. These results provide new techniques for automated proofs of termination.

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Author information

Authors and Affiliations

  1. National Institute of Aerospace, 144 Research Drive, Hampton, Virginia, 23666, USA

    Alfons Geser

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

    Dieter Hofbauer

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

    Johannes Waldmann

Authors
  1. Alfons Geser
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  2. Dieter Hofbauer
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  3. Johannes Waldmann
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Branislav Rovan

  2. Charles University, Prague, Czech Republic

    Peter Vojtáš

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Geser, A., Hofbauer, D., Waldmann, J. (2003). Match-Bounded String Rewriting Systems. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_39

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  • DOI: https://doi.org/10.1007/978-3-540-45138-9_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40671-6

  • Online ISBN: 978-3-540-45138-9

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