References

The curated list of references can be found in https://juliareach.github.io/ReachabilityAnalysis.jl/dev/references/

Theses

• Althoff, Matthias. Reachability analysis and its application to the safety assessment of autonomous cars. Diss. Technische Universität München, 2010.

• Fundamental techniques for the scalable analysis of systems Schilling, Christian

• Formal Verification of Cyber-Physical Systems in the Industrial Model-Based Design Process Nikolaos Kekatos

• Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics Colas Le Guernic

Support functions

• https://arxiv.org/pdf/2002.04086.pdf

Zonotopes

• http://ljk.imag.fr/membres/Antoine.Girard/Publications/hscc2006a.pdf
• http://www.lsv.fr/~fribourg/MPRI_2019_Girard_Zonotopes.pdf
• http://khalilghorbal.info/assets/pdf/papers/cav2010.pdf

Polynomial zonotopes

• https://arxiv.org/abs/1901.01780

Taylor models

http://ceur-ws.org/Vol-2560/paper26.pdf

Hamilton-Jacobi

Underapprox

• https://arxiv.org/pdf/2002.04086.pdf

SOS

Tags: underapproximate, underapproximating, polynomial, semidefinite programming.

• https://github.com/JuliaReach/Reachability.jl/issues/416
• https://dl.acm.org/citation.cfm?id=3178133
• http://lcs.ios.ac.cn/~znj/papers/HSCC2018b.pdf
• https://arxiv.org/abs/1903.07274
• https://arxiv.org/pdf/1903.05311.pdf

Interval methods

• https://hal.archives-ouvertes.fr/hal-01650701/document
• https://www.ennoruijters.nl/imrmc.pdf
• https://ieeexplore.ieee.org/abstract/document/6225315
• https://ieeexplore.ieee.org/abstract/document/7353640
• https://www.ennoruijters.nl/imrmc.pdf

Bernstein methods

• https://dl.acm.org/doi/10.1145/2883817.2883838

Linear HA

• https://ris.utwente.nl/ws/files/116654630/paper3_acm.pdf

Differential inclusions

• https://arxiv.org/abs/2001.11330

Hybrid

• https://www.researchgate.net/publication/318857410_Time-Triggered_Conversion_of_Guards_for_Reachability_Analysis_of_Hybrid_Automata

Other

• https://arxiv.org/abs/2001.00080
• https://link.springer.com/chapter/10.1007/978-3-030-41131-2_6
• https://arxiv.org/abs/2003.05617
• https://arxiv.org/abs/2003.05912

Neural Networks

• https://arxiv.org/pdf/2003.01226.pdf
• https://arxiv.org/abs/1610.06940
• Algorithms for verifying deep neural networks
• https://arxiv.org/pdf/2001.03662.pdf
• http://qav.comlab.ox.ac.uk/papers/hkww17.pdf
• Fast neural network verification via shadow prices. See also the post in AI-facebook.

Conformance testing

• http://ceur-ws.org/Vol-2560/paper26.pdf

Other applications

• https://arxiv.org/pdf/2003.02957.pdf
• https://arxiv.org/pdf/2003.02905.pdf
• https://dl.acm.org/doi/abs/10.1145/996566.996790
• https://arxiv.org/pdf/1904.02765.pdf
• https://arxiv.org/pdf/2002.04192.pdf
• http://www.i6.in.tum.de/Main/Publications/Elguindy2017b.pdf

Delay Differential Equations

• http://lcs.ios.ac.cn/~znj/papers/Over__and_Under_Approximating_Reach_Sets_for_Perturbed_Delay_Differential_Equations__TAC-2020-1.pdf

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• https://ieeexplore.ieee.org/abstract/document/8984475

• https://arxiv.org/abs/2001.11330

• https://link.springer.com/chapter/10.1007/978-3-030-41131-2_6-

• https://www.cs.cmu.edu/afs/cs/user/reids/www/verification/index.html

• http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.538.9218&rep=rep1&type=pdf

• https://ieeexplore.ieee.org/abstract/document/9030138

• https://ieeexplore.ieee.org/abstract/document/9030021

• https://ieeexplore.ieee.org/abstract/document/9030105

• https://hal.archives-ouvertes.fr/hal-02505237/document

• https://ieeexplore.ieee.org/abstract/document/9029572

• https://ieeexplore.ieee.org/abstract/document/9028932

• https://arxiv.org/pdf/2003.07798.pdf

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2020

• Kochdumper, Niklas, and Matthias Althoff. Reachability analysis for hybrid systems with nonlinear guard sets.. Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control. 2020.

• https://dl.acm.org/doi/abs/10.1145/3365365.3382202

• https://dl.acm.org/doi/abs/10.1145/3365365.3382200