The Reachability Problem for Neural-Network Control Systems
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Abstract (arXiv)
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.
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References · 8
- 2013Intriguing properties of neural networkscited by 5,155
- 2014On the Number of Linear Regions of Deep Neural Networkscited by 381
- 2016Understanding Deep Neural Networks with Rectified Linear Unitscited by 257
- 2019Algorithms for Verifying Deep Neural Networkscited by 221
- 2019JuliaReach: a Toolbox for Set-Based Reachabilitycited by 28
- 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
- 2022Reachability In Simple Neural Networkscited by 5
- 2022Verifying And Interpreting Neural Networks using Finite Automatacited by 2
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