On the continuity set of an Omega rational function
LIAFA, Université Paris 7 et CNRS, 2 Place Jussieu 75251 Paris Cedex 05, France;
2 Équipe Modèles de Calcul et Complexité,
3 UMR 6134-Systèmes Physiques de l'Environnement, Faculté des Sciences, Université de Corse, Quartier Grossetti BP52 20250, Corte, France; firstname.lastname@example.org
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 -subset of Σω for some alphabet Σ is the continuity set C(f) of an ω-rational synchronous function f defined on Σω.
Mathematics Subject Classification: 68Q05 / 68Q45 / 03D05
Key words: Infinitary rational relations / omega rational functions / topology / points of continuity / decision problems / omega rational languages / omega context-free languages.
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