The Reachability Problem for Neural-Network Control Systems
<|reference_start|>The Reachability Problem for Neural-Network Control Systems: A control system consists of a plant component and a controller which periodically computes a control input for the plant. We consider systems where the controller is implemented by a feedforward neural network with ReLU activations. The reachability problem asks, given a set of initial states, whether a set of target states can be reached. We show that this problem is undecidable even for trivial plants and fixed-depth neural networks with three inputs and outputs. We also show that the problem becomes semi-decidable when the plant as well as the input and target sets are given by automata over infinite words.<|reference_end|>
@article{schilling2024the,
    title={The Reachability Problem for Neural-Network Control Systems},
    author={Christian Schilling and Martin Zimmermann},
    journal={AISoLA 2023},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.04988},
    primaryClass={cs.LG cs.CC cs.LO cs.SY eess.SY}
}