Computer Science Department
School of Computer Science, Carnegie Mellon University
Invariance of Conjunctions of Polynomial Equalities
Khalil Ghorbal, Andrew Sogokon, André Platzer
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.