On congruences of automata defined by directed graphs

Abstract

Graphs and various objects derived from them are basic essential tools that have been actively used in various branches of modern theoretical computer science. In particular, graph grammars and graph transformations have been very well explored in the literature. We consider finite state automata defined by directed graphs, characterize all their congruences, and give a complete description of all automata of this type satisfying three properties for congruences introduced and considered in the literature by analogy with classical semisimplicity conditions that play important roles in structure theory.