Issue Theoret. Informatics Appl. Volume 39, Number 1, January-March 2005 Imre Simon, the tropical computer scientist Page(s) 217 - 237 DOI 10.1051/ita:2005013

Theoret. Informatics Appl. 39, 217-237 (2005)
DOI: 10.1051/ita:2005013

How expressions can code for automata

Sylvain Lombardy¹ and Jacques Sakarovitch<sup>2

1</sup>  LIAFA (UMR 7089), Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France; lombardy@liafa.jussieu.fr
²  LTCI (UMR 5141), CNRS/ENST, 46 rue Barrault, 75634 Paris Cedex 13, France; sakarovitch@enst.fr

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.

Mathematics Subject Classification. 68Q45, 68Q70

Key words: Finite automata -- regular expression -- derivation of expressions -- quotient of automata.


© EDP Sciences 2005

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