Article

A Method for Invariant Generation for Polynomial Continuous Systems

Authors:

Andrew Sogokon,

Khalil Ghorbal,

Paul B. Jackson,

André PlatzerAuthors Info & Claims

VMCAI 2016: Proceedings of the 17th International Conference on Verification, Model Checking, and Abstract Interpretation - Volume 9583

Pages 268 - 288

https://doi.org/10.1007/978-3-662-49122-5_13

Published: 17 January 2016 Publication History

Abstract

This paper presents a method for generating semi-algebraic invariants for systems governed by non-linear polynomial ordinary differential equations under semi-algebraic evolution constraints. Based on the notion of discrete abstraction, our method eliminates unsoundness and unnecessary coarseness found in existing approaches for computing abstractions for non-linear continuous systems and is able to construct invariants with intricate boolean structure, in contrast to invariants typically generated using template-based methods. In order to tackle the state explosion problem associated with discrete abstraction, we present invariant generation algorithms that exploit sound proof rules for safety verification, such as differential cut$${\text {DC}}$$, and a new proof rule that we call differential divide-and-conquer$${\text {DDC}}$$, which splits the verification problem into smaller sub-problems. The resulting invariant generation method is observed to be much more scalable and efficient than the naïve approach, exhibiting orders of magnitude performance improvement on many of the problems.

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cover image Guide Proceedings

VMCAI 2016: Proceedings of the 17th International Conference on Verification, Model Checking, and Abstract Interpretation - Volume 9583

January 2016

534 pages

ISBN:9783662491218

Editors:
Barbara Jobstmann
EPFL IC-DO, Lausanne, Switzerland
,
K. Rustan M. Leino
Microsoft Research, Redmond, USA

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 January 2016

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Ghorbal KSogokon A(2022)Characterizing positively invariant setsJournal of Symbolic Computation10.1016/j.jsc.2022.01.004113:C(1-28)Online publication date: 1-Nov-2022
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