Abstract. The concept of irreducible automaton is introduced and it is shown that every irreducible automaton is primitive. Reset primitive one-defect automata are proved to be irreducible. It is also shown that Munn–Ponizovsky’s theorem about irreducible representations of semigroups can be used for linear representations of automata.
Keywords: automaton, monoid, semigroup.
Рысцов Игорь Константинович,
кандидат физ.-мат. наук, доцент Национального технического университета Украины «Киевский политехнический институт»,
e-mail: haryst49@gmail.com.