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

  • Khalil Ghorbal
  • Andrew Sogokon
  • André Platzer
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Khalil Ghorbal
    • 1
  • Andrew Sogokon
    • 2
  • André Platzer
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.LFCS, School of InformaticsUniversity of EdinburghEdinburghScotland, UK

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