The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time of the non-negative reals. We show that in the continuous time there are phenomena which are very different from the canonical discrete time domain of the natural numbers.

翻译：Church问题要求构造一个过程：给定输入ω-字符串I与输出ω-字符串O之间的逻辑规范A(I,O)，判断是否存在一个算子F实现该规范，使得对所有输入I均有A(I, F(I))成立。Büchi与Landweber针对MSO规范及有限状态自动机可计算的算子提出了Church问题的求解过程。本文将Church综合问题推广至非负实数连续时间域，并证明连续时间下存在与自然数规范离散时间域截然不同的现象。