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...

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Main Authors: R. Chaudhuri, H. Höft
Format: Article
Language:English
Published: Wiley 1988-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171288000420
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author R. Chaudhuri
H. Höft
author_facet R. Chaudhuri
H. Höft
author_sort R. Chaudhuri
collection DOAJ
description 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.
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institution Kabale University
issn 0161-1712
1687-0425
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publishDate 1988-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-66c36215a47b482eb8bcc72640bfab712025-08-20T03:34:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111235536410.1155/S0161171288000420On rational solution of the state equation of a finite automatonR. Chaudhuri0H. Höft1Department of Computer Science, Eastern Michigan University, Ypsilanti 48197, MI, USADepartment of Computer Science, Eastern Michigan University, Ypsilanti 48197, MI, USAWe 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.http://dx.doi.org/10.1155/S0161171288000420automatastate equationGF(2)rational solutions.
spellingShingle R. Chaudhuri
H. Höft
On rational solution of the state equation of a finite automaton
International Journal of Mathematics and Mathematical Sciences
automata
state equation
GF(2)
rational solutions.
title On rational solution of the state equation of a finite automaton
title_full On rational solution of the state equation of a finite automaton
title_fullStr On rational solution of the state equation of a finite automaton
title_full_unstemmed On rational solution of the state equation of a finite automaton
title_short On rational solution of the state equation of a finite automaton
title_sort on rational solution of the state equation of a finite automaton
topic automata
state equation
GF(2)
rational solutions.
url http://dx.doi.org/10.1155/S0161171288000420
work_keys_str_mv AT rchaudhuri onrationalsolutionofthestateequationofafiniteautomaton
AT hhoft onrationalsolutionofthestateequationofafiniteautomaton