Construction of low-discrepancy point sets of small size by bracketing covers and dependent randomized rounding

In memory of our friend, colleague and former fellow student Manfred Schocker Summary. We provide a deterministic algorithm that constructs small point sets exhibiting a low star discrepancy. The algorithm is based on bracketing and on recent results on randomized roundings respecting hard constraints. It is structurally much simpler than the previous algorithm presented for this problem in [B. Doerr, M. Gnewuch, A. Srivastav. Bounds and constructions for the star discrepancy via δ-covers. J. Complexity, 21:691–709, 2005]. Besides leading to better theoretical run time bounds, our approach also can be implemented with reasonable effort.

Generation of Signals Under Temporal Constraints for CPS Testing

International audienceThis work is concerned with validation of cyber-physical systems (CPS) via sampling of input signal spaces. Such a space is infinite and in general too difficult to treat symbolically, meaning that the only reasonable option is to sample a finite number of input signals and simulate the corresponding system behaviours. It is important to choose a sample so that it best "covers" the whole input signal space. We use timed automata to model temporal constraints, in order to avoid spurious bugs coming from unrealistic inputs and this can also reduce the input space to explore. We propose a method for low-discrepancy generation of signals under temporal constraints recognised by timed au-tomata. The discrepancy notion reflects how uniform the input signal space is sampled and additionally allows deriving validation and performance guarantees. To evaluate testing quality, we also show a measure of uniformity of an arbitrary set of input signals. We describe a prototype tool chain and demonstrate the proposed methods on a Kinetic Battery Model (KiBaM) and a Σ∆ modulator