Preservation of regularity by a term rewrite system (TRS) states that the set of reachable terms from a tree automata (TA) language (aka regular term set) is also a TA language. It is an important and useful property, and there have been many works on identifying classes of TRS ensuring it; unfortunately, regularity is not preserved for restricted classes of TRS like shallow TRS. Nevertheless, ...

In this paper we study control systems whose input sets are quantized, and in particular nite or countable but nowhere dense. We speci cally 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 results on the rechable set of linear quantized systems, and on a particular but interesting class of nonlinear s...

Existing program analysis tools that implement abstraction rely on saturating procedures to compute over-approximations of fixpoints. As an alternative, we propose a new algorithm to compute an over-approximation of the set of reachable states of a program by replacing loops in the control flow graph by their abstract transformer. Our technique is able to generate diagnostic information in case...

We present a set of methods for the verification and control of continuous andhybrid systems, based on the use of individual trajectories. In the first part, we specifythe class of the systems considered and their properties. We start from continuous systemsgoverned by ordinary differential equations to which we add inputs and discrete events,thus constituting a class of hybrid ...

This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of terms reachable by a rewriting relation. The completion algorithm we focus on is parameterized by a set E of equations controlling the precision of the approxima...

We propose a symbolic algorithm for the analysis of the robustness of timed automata, that is the correctness of the model in presence of small drifts on the clocks or imprecision in testing guards. This problem is known to be decidable with an algorithm based on detecting strongly connected components on the region graph, which, for complexity reasons, is not effective in practice. Our symboli...

We give a model of a robot’s finger and we use the methods of the theory of iterated function systems to study the asymptotic reachability set. We provide a technique for the approximation of the asymptotic reachable set and we show an explicit description of such a set in a particular case.

This work is concerned with the algorithmic reachability analysis of continuoustime linear systems with constrained initial states and inputs. We propose an approach for computing an over-approximation of the set of states reachable on a bounded time-interval. The main contribution over previous works is that it allows us to consider systems whose sets of initial states and inputs are given by ...

In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite observations system trajectories. particular, paper focuses on polyhedral sets. We propose data-driven method based one step forward reachable set. For formal verification proposed method, introduce concepts $\lambda$-contractive sets and almost-invariant systems. The ...

BACKGROUND The concept of reachable workspace is closely tied to upper limb joint range of motion and functional capability. Currently, no practical and cost-effective methods are available in clinical and research settings to provide arm-function evaluation using an individual's three-dimensional (3D) reachable workspace. A method to intuitively display and effectively analyze reachable worksp...