A.: Generating polynomial invariants for hybrid systems

Abstract. We present a powerful computational method for automat-ically generating polynomial invariants of hybrid systems with linear continuous dynamics. When restricted to linear continuous dynamical systems, our method generates a set of polynomial equations (algebraic set) that is the best such over-approximation of the reach set, under the assumption that in every eigenvalue a + ib, the constants a and b are interpretation framework over the lattice defined by algebraic sets. Alge-braic sets are represented using canonical Gröbner bases and the lattice operations are effectively computed via appropriate Gröbner basis ma-nipulations.