Abstract : 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 Pi^0_2-subset of X^omega for some alphabet X is the continuity set C(F) of an omega-rational synchronous function F defined on X^omega.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00216624
Contributeur : Olivier Finkel
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Soumis le : vendredi 25 janvier 2008 - 08:57:38
Dernière modification le : vendredi 4 janvier 2019 - 17:32:56
Document(s) archivé(s) le : jeudi 15 avril 2010 - 18:46:17
Olivier Carton, Olivier Finkel, Pierre Simonnet. On the Continuity Set of an omega Rational Function. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2008, 42 ((1)), pp.183-196. 〈ensl-00216624〉
