The Church Synthesis Problem over Continuous Time
<|reference_start|>The Church Synthesis Problem over Continuous Time: 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.<|reference_end|>
@article{rabinovich2024the,
    title={The Church Synthesis Problem over Continuous Time},
    author={Alexander Rabinovich and Daniel Fattal},
    journal={arXiv preprint arXiv:2404.04782},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.04782},
    primaryClass={cs.LO}
}