Languages Representable by Vertex-Labeled Graphs

  • Igor Grunsky
  • Oleksiy Kurganskyy
  • Igor Potapov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


In this paper we study the properties of undirected vertex-labeled graphs and the limitations on the languages that they represent. As a main result of this paper we define the necessary and sufficient conditions for the languages to be representable by a class of undirected vertex-labeled graphs and its subclasses. We assume that all obtained results and techniques are transferable to the case of undirected edge-labeled graphs and might give us similar results. The simplicity of necessary conditions emphasizes the naturalness of the result. The proof of their sufficiency is quite non-trivial and it is based on a new notion of quasi-equivalence, that is significantly different from Myhill-Nerode equivalence and might not be reduced to it.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor Grunsky
    • 1
  • Oleksiy Kurganskyy
    • 1
  • Igor Potapov
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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