Quasivarieties of automata. Connections with quasigroups
\textit{P. J. Higgins} [Math. Nachr. 27, 115-132 (1963; Zbl 0117.259)] gave an invariant characteristic of varieties of many-sorted algebras (cf. \textit{B. I. Plotkin}, \textit{Ts. E. Dididze}, and \textit{E. M. Kublanova} [Kibernetika 1977, No.1, 47-54 (1977; Zbl 0356.94062)] for its application to automata). The corresponding characteristic of quasivarieties, that generalizes Mal'tsev's well-known theorem, can be found in the author's ''Quasivarieties in many-sorted algebras'' [Theses of Brief Communications, Int. Math. Conf., Warsaw 1983, Section II, Algebra, p. 20 (1983)]: A class of many-sorted algebras is a quasivariety if, and only if, it is closed relative to filtered products, is hereditary and contains the identity algebra. In our paper, this characteristic is applied to automata. Our paper consists of three sections. The first two are devoted to quasivarieties of automata. We define classes of automata, saturated relative to input and output signals. Section 3 is devoted to an application of the methods of many-sorted algebras to the theory of quasigroups. This application is founded upon the concept of reversible automaton.
scientific article; zbMATH DE number 4009826
scientific article