Geodesic
On the continuity set of an Omega rational function
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 1, pp. 183-196

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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 Π 2 0 -subset of Σ ω for some alphabet Σ is the continuity set C(f) of an ω-rational synchronous function f defined on Σ ω .

DOI : 10.1051/ita:2007050
Classification : 68Q05, 68Q45, 03D05
Keywords: infinitary rational relations, omega rational functions, topology, points of continuity, decision problems, omega rational languages, omega context-free languages 
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     title = {On the continuity set of an {Omega} rational function},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {183--196},
     publisher = {EDP-Sciences},
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     year = {2008},
     doi = {10.1051/ita:2007050},
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     zbl = {1149.03028},
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Carton, Olivier; Finkel, Olivier; Simonnet, Pierre. On the continuity set of an Omega rational function. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 1, pp. 183-196. doi: 10.1051/ita:2007050

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