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A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8931))

Abstract

This paper presents a theoretical and experimental comparison of sound proof rules for proving invariance of algebraic sets, that is, sets satisfying polynomial equalities, under the flow of polynomial ordinary differential equations. Problems of this nature arise in formal verification of continuous and hybrid dynamical systems, where there is an increasing need for methods to expedite formal proofs. We study the trade-off between proof rule generality and practical performance and evaluate our theoretical observations on a set of heterogeneous benchmarks. The relationship between increased deductive power and running time performance of the proof rules is far from obvious; we discuss and illustrate certain classes of problems where this relationship is interesting.

This material is based upon work supported by the National Science Foundation (NSF) under NSF CAREER Award CNS-1054246, NSF EXPEDITION CNS-0926181, NSF CNS-0931985, by DARPA under agreement number FA8750-12-2-029, as well as the Engineering and Physical Sciences Research Council (UK) under grant EP/I010335/1.

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Authors and Affiliations

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

    Khalil Ghorbal & André Platzer

  2. LFCS, School of Informatics, University of Edinburgh, Edinburgh, Scotland, UK

    Andrew Sogokon

Authors
  1. Khalil Ghorbal
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  2. Andrew Sogokon
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  3. André Platzer
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India

    Deepak D’Souza

  2. Microsoft Research India, 560001, Bangalore, India

    Akash Lal

  3. Department of Computer Science, Aalborg University, Selma Lagerlöfs Vej 300, DK-9220, Aalborg East, Denmark

    Kim Guldstrand Larsen

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Ghorbal, K., Sogokon, A., Platzer, A. (2015). A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets. In: D’Souza, D., Lal, A., Larsen, K.G. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2015. Lecture Notes in Computer Science, vol 8931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46081-8_24

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  • DOI: https://doi.org/10.1007/978-3-662-46081-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46080-1

  • Online ISBN: 978-3-662-46081-8

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