On rational solution of the state equation of a finite automaton
R. Chaudhuri1and H. Höft1
Received21 Jan 1987
Revised25 Jun 1987
Abstract
We prove that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.