The Church Synthesis Problem over Continuous Time
Logic in Computer Science
2025-07-30 v4
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.
Cite
@article{arxiv.2404.04782,
title = {The Church Synthesis Problem over Continuous Time},
author = {Alexander Rabinovich and Daniel Fattal},
journal= {arXiv preprint arXiv:2404.04782},
year = {2025}
}