Affine forms are a common way to represent convex sets of R using
a base of error terms ϵ∈[−1,1]m. Quadratic forms are an
extension of affine forms enabling the use of quadratic error terms ϵiϵj.
In static analysis, the zonotope domain, a relational abstract domain based
on affine forms has been used in a wide set of settings, e.g. set-based
simulation for hybrid systems, or floating point analysis, providing relational
abstraction of functions with a cost linear in the number of errors terms.
In this paper, we propose a quadratic version of zonotopes. We also present a
new algorithm based on semi-definite programming to project a quadratic
zonotope, and therefore quadratic forms, to intervals. All presented material
has been implemented and applied on representative examples.Comment: 17 pages, 5 figures, 1 tabl