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How expressions can code for automata

Published online by Cambridge University Press:  15 March 2005

Sylvain Lombardy  and
Jacques Sakarovitch
Sylvain Lombardy
Affiliation:
LIAFA (UMR 7089), Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France; lombardy@liafa.jussieu.fr
Jacques Sakarovitch
Affiliation:
LTCI (UMR 5141), CNRS/ENST, 46 rue Barrault, 75634 Paris Cedex 13, France; sakarovitch@enst.fr
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Abstract

In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata.
We show here that if an automaton is then sufficiently “decorated”, the combination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.

Keywords

Finite automataregular expressionderivation of expressionsquotient of automata.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 217 - 237
Copyright
© EDP Sciences, 2005

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