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A Differential Operator Approach to Equational Differential Invariants

(Invited Paper)

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Book cover Interactive Theorem Proving (ITP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7406))

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Abstract

Hybrid systems, i.e., dynamical systems combining discrete and continuous dynamics, have a complete axiomatization in differential dynamic logic relative to differential equations. Differential invariants are a natural induction principle for proving properties of the remaining differential equations. We study the equational case of differential invariants using a differential operator view. We relate differential invariants to Lie’s seminal work and explain important structural properties resulting from this view. Finally, we study the connection of differential invariants with partial differential equations in the context of the inverse characteristic method for computing differential invariants.

This material is based upon work supported by the National Science Foundation under NSF CAREER Award CNS-1054246, NSF EXPEDITION CNS-0926181, and under Grant No. CNS-0931985.

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Author information

Authors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, Pittsburgh, USA

    André Platzer

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  1. André Platzer
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Editors and Affiliations

  1. Department of Computer Science, Princeton University, 35 Olden Street, 08540, Princeton, NJ, USA

    Lennart Beringer

  2. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Ave., K1N 6N5, Ottawa, ON, Canada

    Amy Felty

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Platzer, A. (2012). A Differential Operator Approach to Equational Differential Invariants. In: Beringer, L., Felty, A. (eds) Interactive Theorem Proving. ITP 2012. Lecture Notes in Computer Science, vol 7406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32347-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-32347-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32346-1

  • Online ISBN: 978-3-642-32347-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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