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

Random walks on semaphore codes and delay de Bruijn semigroups

We develop a new approach to random walks on de Bruijn graphs over the alphabet $A$ through right congruences on $A^k$, defined using the natural right action of $A^+$. A major role is played by special right congruences, which correspond to semaphore codes and allow an easier computation of the hitting time. We show how right congruences can be approximated by special right congruences.Comment: 34 pages; 10 figures; as requested by the journal, the previous version of this paper was divided into two; this version contains Sections 1-8 of version 1; Sections 9-12 will appear as a separate paper with extra material adde

Graph automata

AbstractMagmoids satisfying the 15 fundamental equations of graphs, namely graphoids, are introduced. Automata on directed hypergraphs are defined by virtue of a relational graphoid. The closure properties of the so-obtained class are investigated, and a comparison is being made with the class of syntactically recognizable graph languages