Abstract Characterization of Input Symbol Semigroups of Universal Hypergraphic Automata
Е. В. Хворостухина, Vladimir Alexandrovich Molchanov · Lobachevskii Journal of Mathematics · 2020
Abstract Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are universal hypergraphic automata. The input symbol semigroup of such automaton is an algebra of mappings which is considered as a derivative algebraic system for such automaton. Semigroup properties of the derivative algebraic system are interconnected with properties of the automaton. Thus, we can obtain a lot of information about a universal hypergraphic automaton studying its input symbol semigroups. In this paper, we found an abstract characterization of universal hypergraphic automata and an abstract characterization of input symbol semigroups of such automata. The results of the paper present effective tools for further analysis of the interrelation of algebraic and elementary properties of universal hypergraphic automata and their input symbol semigroups.