Graph automata: The algebraic properties of abelian relational graphoids

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. © 2011 Springer-Verlag Berlin Heidelberg.