IsaVODEs: interactive verification of cyber-physical systems at scale

Abstract

We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), an open, compositional and extensible framework for the verification of cyber-physical systems. We extend a previous semantic approach with methods and techniques that increase its expressivity, proof automation, and scalability to the level of state-of-the-art deductive verification tools. Our contributions include a user-friendly specification language, a flexible hybrid store model, including vectors and matrices, and separation-logic-style rules for local reasoning with hybrid stores using a novel form of differentiation called framed Fréchet derivatives. The formalisation of correctness specifications with forward predicate transformers, the certification of flows as unique solutions to systems of ordinary differential equations, and invariant reasoning for such systems also contribute to the scalability and usability of our framework. In combination, these features make our framework flexible and adaptable to several verification workflows. A suite of examples and hybrid systems verification benchmarks validate our framework relative to other state-of-the-art approaches.

Metadata

Item Type:	Article
Authors/Creators:	Huerta y Munive, J.J. https://orcid.org/0000-0003-3279-3685 Foster, S. https://orcid.org/0000-0002-9889-9514 Gleirscher, M. https://orcid.org/0000-0002-9445-6863 Struth, G. https://orcid.org/0000-0001-9466-7815 Pardillo Laursen, C. https://orcid.org/0000-0001-7838-2764 Hickman, T. https://orcid.org/0000-0001-7216-1696
Copyright, Publisher and Additional Information:	© The Author(s) 2024. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Keywords:	Cyber-physical systems; Hybrid systems; Program correctness and verification; Interactive theorem proving; Predicate transformers; Lenses
Dates:	Published: December 2024 Published (online): 19 October 2024 Accepted: 29 July 2024
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield)
Depositing User:	Symplectic Sheffield
Date Deposited:	12 Nov 2024 10:10
Last Modified:	12 Nov 2024 10:10
Status:	Published
Publisher:	Springer
Refereed:	Yes
Identification Number:	10.1007/s10817-024-09709-2
Related URLs:	Author
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:219535

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IsaVODEs: interactive verification of cyber-physical systems at scale

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