The paper proposes a simulation-based method for the validation of continuous and hybrid systems, which is built upon the RRT algorithm (Rapidly-exploring Random Trees). We propose a coverage measure, defined as the star discrepancy of the explored points, and use it to guide the simulation process towards the behaviors of interest.

Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a new concept, which we call coarseness, for measuring how blended the elements of S = R ∪ B are. For X ⊆ S, let ∇(X) = ||X ∩ R| − |X ∩ B|| be the bichromatic discrepancy of X. We say that a partition Π = {S1, S2, . . . , Sk} of S is convex if the convex hulls of its members are pairwise disjoint. T...

Many simulation experiments have shown that, in a variety of circumstances, bootstrap tests perform better than current asymptotic theory predicts. Specifically, the discrepancy between the actual rejection probability of a bootstrap test under the null and the nominal level of the test appears to be smaller than suggested by theory, which in any case often yields only a rate of convergence of ...

In a recent paper Cristea and Tichy introduced several types of discrepancies of point sets on the s-dimensional Sierpiński carpet and proved various relations between these discrepancies. In the present paper we prove a general lower bound for those discrepancies in terms of N , the cardinality of the point set, and we give a probabilistic proof for the existence of point sets with “small” dis...

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy principle, in general, does not yield uniform with respect to the data convergence. An a priori choice of the regularization parameter is proposed and justified for ...

Backtracking strategies based on the computation of discrepancies have proved themselves successful at solving large problems. They show really good performance when provided with a high-quality domain-specific branching heuristic (variable and value ordering heuristic), which is the case for many industrial problems. We propose a novel approach (PDS) that allows parallelizing a strategy based ...