On the continuity set of an Omega rational function
Olivier Carton, Olivier Finkel, Pierre Simonnet (2008)
RAIRO - Theoretical Informatics and Applications
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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 has at least one point of continuity and that its continuity set 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....