On algebra of languages representable by vertex-labeled graphs

Authors:
Igor Grunsky;Igor Potapov;Elena Pryanichnikova
Affiliations:
Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, 74 R. Luxemburg St, Donetsk, Ukraine and The Institute of Artificial Intelligence, 84 B.Khmelnitsky, Donetsk ...;Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, UK;The Institute of Artificial Intelligence, 84 B.Khmelnitsky, Donetsk, Ukraine
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

In this paper, we introduce and study an algebra of languages representable by vertex-labeled graphs. The proposed algebra is equipped with three operations: the union of languages, the merging of languages and the iteration. In contrast to Kleene algebra, which is mainly used for edge-labeled graphs, it can adequately represent many properties of languages defined by vertex-labeled graphs and provides a natural translation from vertex-labeled graphs to regular expressions and vice versa.