The Reachability Problem for Neural-Network Control Systems
Machine Learning
2024-12-10 v2 Computational Complexity
Logic in Computer Science
Systems and Control
Systems and Control
Abstract
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.
Keywords
Cite
@article{arxiv.2407.04988,
title = {The Reachability Problem for Neural-Network Control Systems},
author = {Christian Schilling and Martin Zimmermann},
journal= {arXiv preprint arXiv:2407.04988},
year = {2024}
}