Quadratic Zonotopes - An Extension of Zonotopes to Quadratic Arithmetics
Résumé
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 range 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.
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