Languages representable by vertex-labeled graphs

Authors:
Igor Grunsky;Oleksiy Kurganskyy;Igor Potapov
Affiliations:
Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk, Ukraine;Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk, Ukraine;Department of Computer Science, University of Liverpool, Liverpool, UK
Venue:
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Year:
2005

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Abstract

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.