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 domain of the non-negative reals. We show that in the continuous time domain 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，该过程在给定输入ω-串I与输出ω-串O之间的逻辑规约A(I,O)时，能判定是否存在满足如下条件的算子F：对于所有输入I，A(I, F(I))均成立，即该算子实现了规约。Büchi与Landweber针对MSO规约及可由有限状态自动机计算的算子，给出了解决Church问题的过程。本文研究Church综合问题在非负实数连续时间域上的推广。我们证明，在连续时间域中存在与自然数离散时间域截然不同的现象。