The integer programming problem is to decide if a given system of linear inequalities has an integral solution. Recent progress on this algorithmic question has involved techniques from the geometry of numbers, in the celebrated paper of Lenstra [20] and in results of Babai [1], Gr6tschel, Lovfisz and Schrijver [14] and Kannan [16]. One of the things that is apparent in these results is the imp...

The Orbit Problem consists of determining, given a matrix A ∈ Rd×d and vectors x, y ∈ R, whether there exists n ∈ N such that A = y. This problem was shown to be decidable in a seminal work of Kannan and Lipton in the 1980s. Subsequently, Kannan and Lipton noted that the Orbit Problem becomes considerably harder when the target y is replaced with a subspace of R . Recently, it was shown that th...

We describe the Monitoring and Checking (MaC) framework which provides assurance on the correctness of an execution of a real-time system at run-time. Monitoring is performed based on a formal specification of system requirements. MaC bridges the gap between formal specification, which analyzes designs rather than implementations, and testing, which validates implementations but lacks formality...

1.1 Ambient air pollution Uncontrolled dispersion of engineered nanoparticles may affect human health, similarly to what has been found for exposure to particles in ambient air. Particulates (in contrast to gases) are suspected to be the major factor driving the adverse effects of e.g. traffic air pollution. Human exposure to ultrafine particles in the ambient air has been associated with adver...