关于Ω有理函数的连续集
On the Continuity Set of an omega Rational Function
摘要：
本文研究了由Büchi有限状态变换器实现的有理函数的连续性。它已表明Prieur，它可以决定是否这样的功能是连续的。令人惊讶的是，我们在这里证明，它不能决定这样的函数F是否至少有一个连续点，它的连续集C（F）不能计算。在同步有理函数的情况下，我们证明了它的连续集是合理的，它可以计算。进一步证明了X^omega的任意有理Pi^0_2-子集是定义在X^omega上的omega-有理同步函数F的连续集C（F）。
英文摘要：
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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