In this note, we address the reachability of switched linear systems with switching/input constraints. We prove that, under a mild assumption of the feasible switching signals, the reachability set is the reachable subspace of the unconstrained switched system. We also investigate the local reachability for switched systems with input constraints and present a complete criterion for a general c...

We consider the problem of maintaining source sink reachability(st-Reachability), single source reachability(SSR) and strongly connected component(SCC) in an edge decremental directed graph. In particular, we design a randomized algorithm that maintains with high probability1: 1. st-Reachability in Õ(mn) total update time2. 2. st-Reachability in a total update time of Õ(n) in a dense graph. 3. ...

Parametric reasoning is particularly relevant for timed models, but very often leads to undecidability of reachability problems. We propose a parametrised version of Interrupt Timed Automata (an expressive model incomparable to Timed Automata), where polynomials of parameters can occur in guards and updates. We prove that different reachability problems, including robust reachability, are decid...

This paper describes how a number of program-analysis problems can be solved by transforming them to graph-reachability problems. Some of the program-analysis problems that are amenable to this treatment include program slicing, certain dataflow-analysis problems, and the problem of approximating the possible "shapes" that heap-allocated structures in a program can take on. Relationships betwee...

Reachability analysis is one of the most successful methods used in design and validation of protocols for classical communication, whereas the predicate/transition-net formalism is one of the most appropriate formalisms for reachability analysis oriented modelling. Quantum teleportation and dense coding are nonclassical communication protocols widely researched in the field of quantum computin...

Reachability Logic is a recently introduced formalism, which is currently used for defining the operational semantics of programming languages and for stating properties about program executions. In this paper we show how Reachability Logic can be adapted for stating properties of transition systems described by Rewriting-Logic specifications. We propose an automatic procedure for verifying Rew...

The paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete-time systems. Direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability/reachability algorithmandKalman-type algebraic rank criteria. Also the existing geometric crite...

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways to define abstractions for stochastic hybrid systems, which preserve the parameters of stochastic ...

In this paper we analyse the dynamics of one-dimensional piecewise maps (PAMs). We show that one-dimensional PAMs are equivalent to pseudo-billiard or so called “strange billiard” systems. We also show that the more general class of rational functions leads to undecidability of reachability problem for one-dimensional piecewise maps with a finite number of intervals.

A graph H is computable if there is a graph G = (V, E) isomorphic to H where the set V of vertices and the edge relation E are both computable. In this case G is called a computable copy of H. The reachability problem for H in G is, given u, w ∈ V , to decide whether there is a path from u to w. If the reachability problem for H is decidable in all computable copies of H then the problem is int...