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Theory of Computing Systems

, Volume 34, Issue 4, pp 299–336 | Cite as

An Internal Presentation of Regular Graphs by Prefix-Recognizable Graphs

  • D. Caucal
  • T. Knapik
Article

Abstract.

The study of infinite graphs has potential applications in the specification and verification of infinite systems and in the transformation of such systems. Prefix-recognizable graphs and regular graphs are of particular interest in this area since their monadic second-order theories are decidable. Although the latter form a proper subclass of the former, no characterization of regular graphs within the class of prefix-recognizable ones has been known, except for a graph-theoretic one in [2]. We provide here three such new characterizations. In particular, a decidable, language-theoretic, necessary and sufficient condition for the regularity of any prefix-recognizable graph is established. Our proofs yield a construction of a deterministic hyperedge-replacement grammar for any prefix-recognizable graph that is regular.

Keywords

Binary Relation Regular Graph Regular Language Graph Grammar Dependence Level 
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 New York 2001

Authors and Affiliations

  • D. Caucal
    • 1
  • T. Knapik
    • 2
  1. 1.IRISA—CNRS, caucal@irisa.fr FR
  2. 2.ERMIT, Réunion, France knapik@univ-reunion.frFR

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