On the Continuity Set of an omega Rational Function

Details On the Continuity Set of an omega Rational Function On the Continuity Set of an omega Rational Function

2008-01-25

arxiv.org/abs/0801.3912v1

Theoretical Informatics and Applications (1), 42 (2008) 183-196

Computer Science

Computational Complexity

Dedicated to Serge Grigorieff on the occasion of his 60th Birthday

Scientific paper

In this paper, we study the continuity of rational functions realized by B\"uchi 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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