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Journal Articles RAIRO - Theoretical Informatics and Applications (RAIRO: ITA) Year : 2008

On the Continuity Set of an omega Rational Function

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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.
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Dates and versions

ensl-00216624 , version 1 (25-01-2008)

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Olivier Carton, Olivier Finkel, Pierre Simonnet. On the Continuity Set of an omega Rational Function. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2008, 42 ((1)), pp.183-196. ⟨ensl-00216624⟩
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