Related papers: Deciding subspace reachability problems with appli…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
This work is to provide a comprehensive treatment of the relationship between the theory of the generalized (palindromic) eigenvalue problem and the theory of the Sylvester-type equations. Under a regularity assumption for a specific matrix…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the…
We consider a range of geometric stability problems for hypersurfaces of spaceforms. One of the key results is an estimate relating the distance to a geodesic sphere of an embedded hypersurface with integral norms of the traceless Hessian…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
Analysis of cryptographic protocols in a symbolic model is relative to a deduction system that models the possible actions of an attacker regarding an execution of this protocol. We present in this paper a transformation algorithm for such…
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…
This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems,…
Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
In this paper, we begin by constructing global linear maps on (n-2)-dimensional subspaces, derived from the local continuity of linear transformations among central sections of a convex body. Using these linear maps, we subsequently…
In this paper, we address the problem of determining a function in terms of its orbital integrals on Lorentzian symmetric spaces. It has been solved by S. Helgason for even-dimensional isotropic Lorentzian symmetric spaces via a limit…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
The paper deals with the verification of reachability properties in a commonly used state transition model of communication protocols, which consists of finite state machines connected by potentially unbounded FIFO channels. Although simple…
In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
We consider the problem of determining, given x, y in Z^k and a finite set F of affine functions on Z^k, whether y is reachable from x by applying the functions F. We also consider the analogous problem over N^k. These problems are known to…