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Reachability is NP-Complete Even for the Simplest Neural Networks

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Reachability Problems (RP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13035))

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Abstract

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive input/output specifications. We repair some flaws in the original upper and lower bound proofs. We then show that NP-hardness already holds for restricted classes of simple specifications and neural networks with just one layer, as well as neural networks with minimal requirements on the occurring parameters.

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Notes

  1. 1.

    While this paper was being processed, Katz et al. published an extended version of their original paper [9]. Unfortunately, the flaws concerning the upper bound are still present in this version.

  2. 2.

    These problems are repaired in [9], but in a slightly different way than we do.

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Authors and Affiliations

  1. School of Electr. Eng. and Computer Science, University of Kassel, Kassel, Germany

    Marco Sälzer & Martin Lange

Authors
  1. Marco Sälzer
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  2. Martin Lange
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Correspondence to Marco Sälzer .

Editor information

Editors and Affiliations

  1. Liverpool John Moores University, Liverpool, UK

    Paul C. Bell

  2. University of Liverpool, Liverpool, UK

    Patrick Totzke

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Sälzer, M., Lange, M. (2021). Reachability is NP-Complete Even for the Simplest Neural Networks. In: Bell, P.C., Totzke, P., Potapov, I. (eds) Reachability Problems. RP 2021. Lecture Notes in Computer Science(), vol 13035. Springer, Cham. https://doi.org/10.1007/978-3-030-89716-1_10

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  • DOI: https://doi.org/10.1007/978-3-030-89716-1_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89715-4

  • Online ISBN: 978-3-030-89716-1

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