Relatively Elementary Definability of the Class of Universal Graphic Semiautomata in the Class of Semigroups

Automata theory is a branch of mathematical cybernetics that studies data conversion devices involved in many applied problems. This article considers automata with no output signals, called semiautomata. With regard to specific problems, semiautomata (whose sets of states are endowed with an additional mathematical structure consistent with the semiautomaton's transition function) are considered. This study investigates semiautomata over graphs (known as graphic semiautomata), whose sets of states are endowed with the mathematical structure of a graphic. Universal graphic semiautomaton Atm(G) is the universally attracting object in the category of semiautomata whose sets of states are endowed with the structure of graph G, preserved by the transition function of the semiautomaton. The semigroup of input signals of that semiautomaton has the form S(G) = End G. This study considers the problem of relatively elementary definability of the class of universal graphic semiautomata over reflexive quasi-acyclic graphs in the class of semigroups, as well as the applications of relatively elementary definability.