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Match-Bounded String Rewriting Systems

  • Alfons Geser
  • Dieter Hofbauer
  • Johannes Waldmann
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Regular Language Cryptographic Protocol Minimal Height Uniform Termination Note Comp 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alfons Geser
    • 1
  • Dieter Hofbauer
    • 2
  • Johannes Waldmann
    • 3
  1. 1.National Institute of AerospaceHamptonUSA
  2. 2.Fachbereich Mathematik/InformatikUniversität KasselKasselGermany
  3. 3.Fakultät für Mathematik und InformatikUniversität LeipzigLeipzigGermany

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