Three linearization techniques for multivariate polynomials in static analysis using convex polyhedra

We present three linearization methods to over-approximate non-linear multivariate polynomials with convex polyhedra. The first one is based on the substitution of some variables by intervals. The principle of the second linearization technique is to express polynomials in the Bernstein basis and deduce a polyhedron from the Bernstein coefficients. The last method is based on Handelman’s theorem and consists in using products of constraints of a starting polyhedron to over-approximate a polynomial. As a part of the VERASCO project, the goal is to prove such methods with the proof assistant Coq.