The Reachability Problem for Neural-Network Control Systems

Christian Schilling; Martin Zimmermann

doi:10.1007/978-3-031-73741-1_27

The Reachability Problem for Neural-Network Control Systems

Christian Schilling^*, Martin Zimmermann

^*Kontaktforfatter

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

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.

Originalsprog	Engelsk
Titel	Bridging the Gap Between AI and Reality - 1st International Conference, AISoLA 2023, Selected Papers
Redaktører	Bernhard Steffen
Antal sider	15
Forlag	Springer Science+Business Media
Publikationsdato	2025
Sider	455-469
ISBN (Trykt)	9783031737404
DOI	https://doi.org/10.1007/978-3-031-73741-1_27
Status	Udgivet - 2025
Begivenhed	1st International Symposium on Leveraging Applications of Formal Methods, AISoLA 2023 - Crete, Grækenland Varighed: 23 okt. 2023 → 28 okt. 2023

Konference

Konference	1st International Symposium on Leveraging Applications of Formal Methods, AISoLA 2023
Land/Område	Grækenland
By	Crete
Periode	23/10/2023 → 28/10/2023

Navn	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Vol/bind	14129 LNCS
ISSN	0302-9743

Bibliografisk note

Publisher Copyright:
© The Author(s) 2025.

Adgang til dokumentet

10.1007/978-3-031-73741-1_27

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Citationsformater

Schilling, Christian ; Zimmermann, Martin. / The Reachability Problem for Neural-Network Control Systems. Bridging the Gap Between AI and Reality - 1st International Conference, AISoLA 2023, Selected Papers. red. / Bernhard Steffen. Springer Science+Business Media, 2025. s. 455-469 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 14129 LNCS).

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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.",

author = "Christian Schilling and Martin Zimmermann",

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Schilling, C & Zimmermann, M 2025, The Reachability Problem for Neural-Network Control Systems. i B Steffen (red.), Bridging the Gap Between AI and Reality - 1st International Conference, AISoLA 2023, Selected Papers. Springer Science+Business Media, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), bind 14129 LNCS, s. 455-469, 1st International Symposium on Leveraging Applications of Formal Methods, AISoLA 2023, Crete, Grækenland, 23/10/2023. https://doi.org/10.1007/978-3-031-73741-1_27

The Reachability Problem for Neural-Network Control Systems. / Schilling, Christian ; Zimmermann, Martin.
Bridging the Gap Between AI and Reality - 1st International Conference, AISoLA 2023, Selected Papers. red. / Bernhard Steffen. Springer Science+Business Media, 2025. s. 455-469 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 14129 LNCS).

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

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Schilling C , Zimmermann M. The Reachability Problem for Neural-Network Control Systems. I Steffen B, red., Bridging the Gap Between AI and Reality - 1st International Conference, AISoLA 2023, Selected Papers. Springer Science+Business Media. 2025. s. 455-469. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 14129 LNCS). doi: 10.1007/978-3-031-73741-1_27

The Reachability Problem for Neural-Network Control Systems

Abstract

Konference

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AUB Link

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