Related papers: A Logical Product Approach to Zonotope Intersectio…
Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections…
We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using…
Situational awareness for connected and automated vehicles describes the ability to perceive and predict the behavior of other road-users in the near surroundings. However, pedestrians can become occluded by vehicles or infrastructure,…
Characterizing hybrid ASP solving in a generic way is difficult since one needs to abstract from specific theories. Inspired by lazy SMT solving, this is usually addressed by treating theory atoms as opaque. Unlike this, we propose a…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Template abstract domains allow to express more interesting properties than classical abstract domains. However, template generation is a challenging problem when one uses template abstract domains for program analysis. In this paper, we…
This article presents a new numerical abstract domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form…
Set operations are well understood for convex sets but become considerably more challenging in the non-convex case due to the loss of structural properties in their representation. Constrained polynomial zonotopes (CPZs) offer an effective…
Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on the error between the abstract neural network and the concrete…
It was previously shown that control-flow refinement can be achieved by a program specializer incorporating property-based abstraction, to improve termination and complexity analysis tools. We now show that this purpose-built specializer…
We derive a mixed integer nonlinear programming formulation for the problem of finding a convex polygon with a given number of vertices that is small (diameter at most one) and has maximum perimeter. The formulation is based on a geometric…
This paper presents new methods for set-valued state estimation of nonlinear discrete-time systems with unknown-but-bounded uncertainties. A single time step involves propagating an enclosure of the system states through the nonlinear…
We study a class of convex bodies called operatopes that are obtained by taking Minkowski sums of affine images of an operator norm ball. This notion generalizes that of zonotopes which are Minkowksi sums of line segments. Taking the limit…
In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…
Translating continuous control system models into finite automata allows us to use powerful discrete tools to synthesize controllers for complex specifications. The abstraction construction step is unfortunately hamstrung by high runtime…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…
Abstract interpretation is a method to automatically find invariants of programs or pieces of code whose semantics is given via least fixed-points. Up-to techniques have been introduced as enhancements of coinduction, an abstract principle…
Weakly stationary random processes of $k$-dimensional affine subspaces (flats) in $\mathbb{R}^n$ are considered. If $2k\geq n$, then intersection processes are investigated, while in the complementary case $2k<n$ a proximity process is…
A new efficient approach to the analysis of nonlinear higher-spin equations, that treats democratically auxiliary spinor variables $Z_A$ and integration homotopy parameters in the non-linear vertices of the higher-spin theory, is developed.…