Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations

  • Khalil Ghorbal
  • Andrew Sogokon
  • André Platzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8723)


In this paper we seek to provide greater automation for formal deductive verification tools working with continuous and hybrid dynamical systems. We present an efficient procedure to check invariance of conjunctions of polynomial equalities under the flow of polynomial ordinary differential equations. The procedure is based on a necessary and sufficient condition that characterizes invariant conjunctions of polynomial equalities. We contrast this approach to an alternative one which combines fast and sufficient (but not necessary) conditions using differential cuts for soundly restricting the system evolution domain.


Algebraic Differential Equation Polynomial Vector Proof Rule Ascend Chain Condition Darboux Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

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 EdinburghEdinburghUK

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