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arXiv · 2404.04782

The Church Synthesis Problem over Continuous Time

Alexander Rabinovich·Daniel Fattal
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Abstract

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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Alexander Rabinovich, Daniel Fattal. 2024-04-07. The Church Synthesis Problem over Continuous Time. https://doi.org/10.46298/lmcs-21(3%3A8)2025

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