We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gi...

In this paper we present a new concept of robot-dependent reachability map (RDReachMap) for mobile platforms. In heterogeneous multi-robot systems, the reachability limit of robots motion and actuation must be considered when assigning tasks to them. We created an algorithm that generates those reachability maps, separating regions that can be covered by a robot from the unreachable ones, using...

We investigate the computational power of several models of dynamical systems under infinitesimal perturbations of their dynamics. We consider in our study models for discrete and continuous time dynamical systems: Turing machines, Piecewise affine maps, Linear hybrid automata and Piecewise constant derivative systems (a simple model of hybrid systems). We associate with each of these models a ...

Even though many attempts have been made to define the boundary between decidable and undecidable hybrid systems, the affair is far from being solved. More and more low dimensional systems are being shown to be undecidable with respect to reachability, and many open problems in between are being discovered. In this paper, we present various two dimensional hybrid systems for which the reachabil...

The theory of Well Structured Transition Systems, (WSTS) allows the automatical verification of safety properties of infinite-state systems, such that parts of reachability sets can be finitely represented [7, 11, 10]. Termination, boundedness and coverability are decidable for WSTS [4, 5, 9]. As Petri nets are WSTS, the previous properties are decidable. For complete WSTS [10], the Karp and Mi...

We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gi...

3 IO Automaton 2 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Reachability and invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.3 System traces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.4 Traces versus reachability . . . . . . . . . . . . . . . . . . . . . . . . . ....