Considering an initial set of terms E, a rewriting relation R and a goal set of terms Bad, reachability analysis in term rewriting tries to answer to the following question: does there exists at least one term of Bad that can be reached from E using the rewriting relation R? Some of the approaches try to show that there exists at least one term of Bad reachable from E using the rewriting relati...

A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this question, we show that the moments evolution in any generic network can be either approximated or, under suitable assumptions, computed exactly as the solution of a...

We present a technique to verify safety properties of linear systems (possibly time varying) using very few simulations. For a linear system of dimension n, our technique needs n+ 1 simulation runs. This is in contrast to current simulation based approaches, where the number of simulations either depends upon the number of vertices in the convex polyhedral initial set, or on the proximity of th...

In this paper we study control systems whose input sets are quantized. We speciically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some recent results on the reachable set of linear quantized systems, and study in detail a particular but interesting class of nonlinear systems, forming the discre...

A model of stock market dynamics is analyzed using a new approach to uncertainty treatment. The problem of uncertainty is formulated in deterministic way, using the differential inclusions as the main modeling tool. This results in the shape of the reachable set for the model trajectory, namely the possible extreme values of the stock demand and price. The results of example analysis are shown,...

The numerical stability of a recent QR-based fast least squares algorithm is established from a backward stability perspective. The paper introduces a stability domain approach applicable to any least squares algorithm, so constructed from the set of reachable states in exact arithmetic. The error propagation question is shown to be subordinate to a backward consistency constraint, which requir...

We consider the analysis of in nite half-duplex systems which consists of nite state machines that communicate over unbounded channels. The property half-duplex for two machines and two channels (one in each direction) says that each reachable state has at least one channel empty. The contributions of this paper are (a) to give a nite description of the reachability set of such systems, which h...

Current symbolic techniques for the automated reasoning on undecidable hybrid automata, force to choose between the refinement of either an overapproximation or an underapproximation of the set of reachable states. When the analysis of branching temporal properties is considered, the literature has developed a number of abstractions techniques based on the simulation preorder, that allow the pr...

One often wishes for the ability to formally analyze large-scale systems—typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used ...

We discuss the calculation of discriminating kernel for the discrete-time dynamic game and continuous-time dynamic game (namely differential game) using the viability kernel and reachable set. For the discrete-time dynamic game, we give an approximation of the viability kernel by the maximal reachable set. Then, based on the relationship between viability and discriminating kernels, we propose ...