The Reachability Problem for Neural-Network Control Systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912147525599232 |
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| author | Schilling, Christian Zimmermann, Martin |
| author_facet | Schilling, Christian Zimmermann, Martin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_04988 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Reachability Problem for Neural-Network Control Systems Schilling, Christian Zimmermann, Martin Machine Learning Computational Complexity Logic in Computer Science Systems and Control 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. |
| title | The Reachability Problem for Neural-Network Control Systems |
| topic | Machine Learning Computational Complexity Logic in Computer Science Systems and Control |
| url | https://arxiv.org/abs/2407.04988 |