RAIRO - Theoretical Informatics and Applications

Table of Contents - January 2005 - Volume 39, Issue 01 (Imre Simon, the tropical computer scientist)  

Research Article

How expressions can code for automata

Lombardy, Sylvaina1 and Sakarovitch, Jacquesa2

a1 LIAFA (UMR 7089), Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France; lombardy@liafa.jussieu.fr

a2 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.

(Online publication March 15 2005)

Key Words:

  • Finite automata;
  • regular expression;
  • derivation of expressions;
  • quotient of automata.

Mathematics Subject Classification:

  • 68Q45;
  • 68Q70