Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations

Khalil Ghorbal (1) , Andrew Sogokon (2) , André Platzer (1)

1 CMU - Carnegie Mellon University [Pittsburgh]
2 LFCS - Laboratory for the Foundations of Computer Science [Edinburgh]

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.

Domaines: Calcul formel [cs.SC]; Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]; Systèmes dynamiques [math.DS]

Khalil Ghorbal, Andrew Sogokon, André Platzer. Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations. Static Analysis - 21st International Symposium, SAS 2014, Munich, Germany, September 11-13, 2014. Proceedings, 2014, Munich, Germany. pp.151--167, ⟨10.1007/978-3-319-10936-7_10⟩. ⟨hal-01660906⟩