Automata and automata mappings of semigroups

TL;DR

This paper explores two algebraic models of automata, analyzing their relationships and implications for decomposition theory and group theory, with potential impacts on formal language theory.

Contribution

It introduces a new automata model and investigates its connection to cascade connections of traditional automata, expanding the theoretical framework.

Findings

Established links between the new automata model and cascade connections

Enhanced understanding of automata decomposition in algebraic terms

Potential applications in group theory and formal languages

Abstract

The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are related to cascade connections of automata of the first type. The introduced automata play a significant role in group theory and, hopefully, in the theory of formal languages.