Let P be a set of n points in the plane where each point p is associated with radius \(r_p>0\). The transmission graph \(G=(P,E)\) defined as directed such that E contains an edge from to q if and only \(|pq|\le r_p\) for any two P, |pq| denotes Euclidean distance between q. In this paper, we present data structure size \(O(n^{5/3})\) can check \(O(n^{2/3})\) time there path G points. This firs...

Reachability and observability criteria are obtained for 2D continuous-discrete time-variable Attasi type systems by using suitable 2D reachability and observability Gramians. Necessary and sufficient conditions of reachability and observability are derived for time-invariant systems. The duality between the two concepts is emphasized as well as their connection with the minimality of these sys...

Positive reachability and positive observability of positive linear systems on time scales are studied. Differential and integral calculus on time scales allows for unified treatment of continuousand discrete-time systems. Reachability and observability graphs for positive systems are introduced. They are used to characterize positive reachability and positive observability for systems on homog...

Reachability testing is a technique for testing concurrent programs. Reachability testing derives test sequences on-the-fly as the testing process progresses, and can be used to systematically exercise all the behaviors of a program. The main contribution of this paper is a general model for reachability testing. This model allows reachability testing to be applied to many different types of co...

We consider infinite state reactive systems specified by using linear constraints over the integers, and we address the problem of verifying safety properties of these systems by applying reachability analysis techniques. We propose a method based on program specialization, which improves the effectiveness of the backward and forward reachability analyses. For backward reachability our method c...

We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that nice reachability analysis may be reduced to the reachability analysis of a specific...

Reachability analysis is a general approach to analyze Petri nets, but the state space explosion often permits its application. In the eld of performance analysis of stochastic Petri nets, modular representations of reachability graphs using Kronecker algebra have been successfully applied. This paper describes how a Kronecker representation of the reachability graph is employed for exploration...