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Affine Systems of ODEs in Isabelle/HOL for Hybrid-Program Verification

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Software Engineering and Formal Methods (SEFM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12310))

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Abstract

We formalise mathematical components for solving affine and linear systems of ordinary differential equations in Isabelle/HOL. The formalisation integrates the theory stacks of linear algebra and analysis and substantially adds content to both of them. It also serves to improve extant verification components for hybrid systems by increasing proof automation, removing certification procedures, and decreasing the number of proof obligations. We showcase these advantages through examples.

This work was funded by CONACYT’s scholarship no. 440404.

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Acknowledgements

The author wishes to thank the reviewers for their insightful comments. He also thanks Georg Struth, Harsh Beohar, Rayna Dimitrova, Kirill Bogdanov and Michael Foster for discussions.

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Authors and Affiliations

  1. The University of Sheffield, Western Bank, Sheffield, S10 2TN, UK

    Jonathan Julián Huerta y Munive

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  1. Jonathan Julián Huerta y Munive
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Correspondence to Jonathan Julián Huerta y Munive .

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Editors and Affiliations

  1. Informatica, Centrum voor Wiskunde en Informatica (CWI), Amsterdam, The Netherlands

    Frank de Boer

  2. Department of Computer Science, Nazarbayev University, Astana, Kazakhstan

    Antonio Cerone

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Huerta y Munive, J.J. (2020). Affine Systems of ODEs in Isabelle/HOL for Hybrid-Program Verification. In: de Boer, F., Cerone, A. (eds) Software Engineering and Formal Methods. SEFM 2020. Lecture Notes in Computer Science(), vol 12310. Springer, Cham. https://doi.org/10.1007/978-3-030-58768-0_5

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  • DOI: https://doi.org/10.1007/978-3-030-58768-0_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58767-3

  • Online ISBN: 978-3-030-58768-0

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