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


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.


Binary Relation Regular Graph Regular Language Graph Grammar Dependence Level 
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Copyright information

© Springer-Verlag New York 2001

Authors and Affiliations

  • D. Caucal
    • 1
  • T. Knapik
    • 2
  2. 2.ERMIT, Réunion, France knapik@univ-reunion.frFR

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