On the Continuity Set of an omega Rational Function

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dc.creatorCarton, Olivier
dc.creatorFinkel, Olivier
dc.creatorSimonnet, Pierre
dc.date2008-01-25
dc.date.accessioned2026-07-07T08:56:27Z
dc.date.available2026-07-07T08:56:27Z
dc.descriptionIn 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.
dc.descriptionDedicated to Serge Grigorieff on the occasion of his 60th Birthday
dc.identifierhttps://arxiv.org/abs/0801.3912
dc.identifierhttp://arxiv.org/abs/0801.3912
dc.identifierTheoretical Informatics and Applications (1), 42 (2008) 183-196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146619
dc.subjectComputational Complexity
dc.subjectLogic in Computer Science
dc.titleOn the Continuity Set of an omega Rational Function
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