On rational solution of the state equation of a finite automaton
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1988-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000420 |
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |