Quadratic Zonotopes:An extension of Zonotopes to Quadratic Arithmetics

Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$. 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

Fine-Tuning the Accuracy of Numerical Computations in Avionics Automatic Code Generators

International audienceMost of safety-critical embedded software, such as y-by-wire control programs, performs a lot of oating-point computations. High level specications are expressed in a formal model edited manually in SCADE through a graphical interface. It generally handles numerical variables and constants as if they were ideal real numbers. This work, for the purpose of numerical accuracy analysis, presents a new version of an Automatic Code Generator (ACG). This tool transforms high-level models into C codes and performs static computations by using multiple-precision arithmetic. This article describes a successful way of controlling computation accuracy of numerical constants in an Automatic Code Generator. An accuracy analysis on numerical constant values is presented in a case study

Quadratic Zonotopes

International audienc