RU
On the \(K\)-finite generation of precomplete classes of linear automata
Biryukova V. A.
Received: 04 Jun 2026 Revised: 09 Jun 2026 Accepted: 10 Jun 2026
Published: 2026, vol. 30, issue 2, pp. 82–100
Abstract
We study the problem of \(K\)-finite generation for precomplete classes of linear automata over the field \(E_2\). It is proved that the classes not belonging to the \(A\)-criterial system are not \(K\)-finitely generated. In addition, a countable series of \(K\)-closed classes that are \(K\)-finitely generated is found. It is also shown that any \(K\)-precomplete class which is not \(K\)-finitely generated is \(A\)-complete.
Keywords: finite automaton, linear automaton, closed class, precomplete class, composition operations, $A$-closure, $K$-finite generation, bases of closed classes.
BibTeX
@article{IS-Biryukova2026,
author = {Biryukova, Veronika Andreevna},
title = {{On the $K$-finite generation of precomplete classes of linear automata}},
journal = {Intelligent Systems. Theory and Applications},
year = {2026},
volume = {30},
number = {2},
pages = {82--100},
}
AMSBIB
\Bibitem{IS-Biryukova2026}
\by V.\,A.~Biryukova
\paper On the $K$-finite generation of precomplete classes of linear automata
\jour Intelligent Systems. Theory and Applications
\yr 2026
\vol 30
\issue 2
\pages 82--100
\lang In Russian