| Issue |
RAIRO-Theor. Inf. Appl.
Volume 42, Number 1, January-March 2008
A nonstandard spirit among computer scientists:a tribute to Serge Grigorieff at the occasion of his 60th birthday
|
|
|---|---|---|
| Page(s) | 183 - 196 | |
| DOI | https://doi.org/10.1051/ita:2007050 | |
| Published online | 18 January 2008 | |
On the continuity set of an Omega rational function
1
LIAFA, Université Paris 7 et CNRS, 2 Place Jussieu 75251 Paris Cedex 05, France;
Olivier.Carton@liafa.jussieu.fr
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;
simonnet@univ-corse.fr
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.
© EDP Sciences, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.