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On the continuity set of an Omega rational function

Published online by Cambridge University Press:  18 January 2008

Olivier Carton
LIAFA, Université Paris 7 et CNRS, 2 Place Jussieu 75251 Paris Cedex 05, France;
Olivier Finkel
Équipe Modèles de Calcul et Complexité,
Pierre Simonnet
UMR 6134-Systèmes Physiques de l'Environnement, Faculté des Sciences, Université de Corse, Quartier Grossetti BP52 20250, Corte, France;
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In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed. Furthermore we prove that any rational ${\bf \Pi}^0_2$-subset of Σω for some alphabet Σ is the continuity set C(f) of an ω-rational synchronous function f defined on Σω.

Research Article
© EDP Sciences, 2007

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