Automata diagram for finite groups - Fong, Wan Heng; Gan, Yee Siang; Sarmin, Nor Haniza; Turaev, Sherzod (2013)
Recently, automata have been related to group theory by using some modification devices. These modification devices are namely deterministic finite automata and modified Watson-Crick finite automata. The automata can be linked to group theory when some automaton diagrams are drawn to recognize the data given in the Cayley table for the groups. Thus, the properties of groups can also be analyzed from the automaton diagrams. In this paper, the formal definitions for modified finite automata and modified Watson-Crick finite automata over the general case of finite groups are given. In addition, theorems are presented for the determination of a group by using the automaton diagram, and for the recognition of automata devices for groups. Lastly, the properties of centralizer of a group resulting from the analysis of automaton diagrams are also presented.