Directed graph in finite automata over finite groups

Abstract

Automata can be related to group theory by using modi- fied deterministic finite automata. These modification devices are then used to study various groups. In the study of automata and group the- ory, some properties of Abelian groups in terms of automaton diagrams are developed. An automaton diagram is also called a directed graph with labelled edge. In this paper, we introduced modified deterministic finite automata to investigate some properties of finite groups. An ex- ample which illustrates the recognition pattern of modified deterministic finite automata over a finite group is given. We show that a non-empty set recognised by a modified deterministic finite automaton under some conditions is a group. In addition, the recognition pattern of modified deterministic finite automata over finite groups is also generalised.