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Deleting String Rewriting Systems Preserve Regularity

  • Dieter Hofbauer
  • Johannes Waldmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2710)

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 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].

Keywords

Regular Language Canonical System Tree Automaton Pivot Rule Bubble Sort 
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

  • Dieter Hofbauer
    • 1
  • Johannes Waldmann
    • 2
  1. 1.Fachbereich Mathematik/InformatikUniversität KasselKasselGermany
  2. 2.Fakultät für Mathematik und InformatikUniversität LeipzigLeipzigGermany

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