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On the Continuity Set of an omega Rational Function

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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Contributor : Olivier Finkel Connect in order to contact the contributor
Submitted on : Friday, January 25, 2008 - 8:57:38 AM
Last modification on : Thursday, September 29, 2022 - 2:58:07 PM
Long-term archiving on: : Thursday, April 15, 2010 - 6:46:17 PM


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  • HAL Id : ensl-00216624, version 1
  • ARXIV : 0801.3912


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⟩



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