Part 3. Mathematical models

The problem of $ K $-finite generation for precomplete classes of linear automata constituting an $A$-criterion system in the space of linear automata

V. A. Biryukova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This article considers the problem of $K$- and $A$-finite generation for precomplete classes of linear automata operating over the Galois field consisting of two elements. The set of all studied classes is the $A$-criterion system in the class of linear automata. A finite basis was presented for each class under consideration.

Keywords: finite automaton, linear automaton, composition operation, feedback operation, completeness, closed class, precomplete class, $K$-finitely generated class, $A$-finitely generated class.