International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 425-428
doi:10.1155/S0161171286000546
A topology for automata. II
Arun K. Srivastava1
and Wagish Shukla2
1Department of Mathematics, Banaras Hindu University, Varansi, India
2Department of Mathematics, Indian Institute of Technology, New Delhi, India
Abstract
A topology on the state set of an automaton is considered and it is shown that under this topology, genetically closed subsets and primaries, in the sense of Bavel [1] turn out to be precisely the regular closed subsets and minimal regular closed subsets respectively. The concept of a compact automaton is introduced and it is indicated that it can be viewed as a generalization of a finite automaton. Included also is an observation showing that our topological considerations can help recover some of the results of Dörfler [2].