Languages recognized by a class of finite automata

We consider automata defined by left multiplications in graph algebras, and describe all languages recognized by these automata in terms of combinatorial properties of words which belong to these languages, regular expressions and linear grammars defining these languages. This description is applied to investigate closure properties of the obtained family of languages

On congruences of automata defined by directed graphs

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