We define several abstract semantics for the static analysis of finite precision computations,
that bound not only the ranges of values taken by numerical variables of a program, but also …

A desirable property of control systems is robustness to inputs, when small perturbations of
the inputs of a system will cause only small perturbations on outputs. This property should …

We define and study a new abstract domain which is a fine-grained combination of
zonotopes with (sub-) polyhedric domains such as the interval, octagon, linear template or …

We study the problem of formally verifying the robustness to adversarial examples of support
vector machines (SVMs), a major machine learning model for classification and regression …

Reachability analysis, in general, is a fundamental method that supports formally-correct
synthesis, robust model predictive control, set-based observers, fault detection, invariant …

Computing a tight inner approximation of the range of a function over some set is notoriously
difficult, way beyond obtaining outer approximations. We propose here a new method to …

We often need to deal with information that contains both interval and probabilistic
uncertainties. P-boxes and Dempster–Shafer structures are models that unify both kind of …

In this thesis, we present the three novel set representations sparse polynomial zonotopes,
constrained polynomial zonotopes, and the Z-representation of polytopes. One major …

Existing neural network verifiers compute a proof that each input is handled correctly under
a given perturbation by propagating a symbolic abstraction of reachable values at each …

We study the certification of stability properties, such as robustness and individual fairness,
of the k-Nearest Neighbor algorithm (kNN). Our approach leverages abstract interpretation …