On a superclass of A-grammars

In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of finite alphabet $\mathcal{A}$. We will call such grammars graph-generated grammars or $\mathrm{G}$-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, $\mathrm{G}$-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing $\mathrm{G}$-grammar which generate the language recognized by deterministic finite automaton. Moreover, we will show that the class of languages generated by $\mathrm{G}$-grammars is a proper superset of regular languages.