Abstract
Automata operating on arbitrary graphs were introduced in a previous paper by virtue of a particular instance of an abelian relational graphoid. As it is indicated in the same paper, in order to construct a graph automaton it is necessary and sufficient that the relations over the Kleene star of the state set constitute a graphoid. In this respect, various different versions of graph automata arise corresponding to the specific relational graphoid that is employed. We prove that the generation of an abelian graphoid by a set Q implies the partitioning of Q into disjoint abelian groups and vise versa.
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Kalampakas, A. (2011). Graph Automata: The Algebraic Properties of Abelian Relational Graphoids. In: Kuich, W., Rahonis, G. (eds) Algebraic Foundations in Computer Science. Lecture Notes in Computer Science, vol 7020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24897-9_8
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DOI: https://doi.org/10.1007/978-3-642-24897-9_8
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