To develop efficient algorithms for the reachability analysis of timed automata, a promising approach is to use binary decision diagrams (BDDs) as data structure for the representation of the explored state space. The size of a BDD is very sensitive to the ordering of the variables. We use the communication structure to deduce an estimation for the BDD size. In our experiments, this guides the ...

We examine the convergence properties of a level set algorithm designed to track evolving interfaces; in particular, its convergence properies on a series of two and three dimensional backwards reachable sets whose flow fields involve kink formation (sharp features) and, in some cases, rarefaction fans introduced by input parameters in the dynamics. The chosen examples have analytic solutions t...

We have a new proof of the lower bound that k-set agreement requires f/k + 1 rounds in a synchronous, message-passing model with f crash failures. The proof involves constructing the set of reachable states, proving that these states are highly connected, and then appealing to a well-known topological result that high connectivity implies that set agreement is impossible. We construct the set o...

In this paper, fuzzy initial value problems for modelling aspects of uncertainty in dynam­ ical systems are introduced and interpreted from a probabilistic point ofview. Due to the uncertainty incorporated in the model, the behavior of dynamical systems modelIed in this way will generally not be unique. Rather, we obtain a large set of trajectories which are more or less compatible with the des...

The paper presents an approach to find contact points on an object surface that are reachable by a given hand and such that the resulting grasp satisfies the force-closure condition. This is a very common problem that still requires a practical solution. The proposed method is based on the computation of a set of independent contact regions on the object boundary such that a finger contact on e...

In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is conver...

Reachable set computation is an important technique for the verification of safety properties dynamical systems. In this paper, we investigate reachable discrete nonlinear systems based on parallelotope bundles. The algorithm relies computing upper bound supremum a function over rectangular domain, which has been traditionally done using Bernstein polynomials. We strive to remove manual step te...