连续时间下的丘奇综合问题
The Church Synthesis Problem over Continuous Time
AI总结：
该研究将丘奇综合问题推广至非负实数连续时间域，发现连续时间域存在与标准离散自然数域截然不同的现象，拓展了该问题的研究范畴。
摘要：
丘奇问题要求构建一种流程：给定输入ω-串I与输出ω-串O之间的逻辑规范A(I,O)，判断是否存在算子F，使得对所有输入I都满足A(I,F(I))，以此实现该规范。Buchi和Landweber提出了一种流程，可求解MSO规范、且算子可由有限状态自动机计算的丘奇问题。我们研究将丘奇综合问题推广到非负实数的连续时间域的情况。我们证明，在连续时间域中存在与自然数这一标准离散时间域截然不同的现象。
英文摘要：
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.
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