In this paper we present a framework for carrying out counterexample guided abstraction-refinement (CEGAR) for systems modelled as hybrid automata. The main difference, between our approach and previous proposals for CEGAR for hybrid automata, is that we consider the abstractions to be hybrid automata as well. We present a counterexample guided abstraction refinement method for systems modelled...

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with periods smaller than a certain value converge to zero. Moreover, ...

Within hybrid systems theory, o-minimal automata are often considered on the border between decidability and undecidability. In such classes of hybrid automata, the constraint of having only constant reset upon discrete jumps is a strong limitation for their applicability: hence, an important issue for both theoreticians and practitioners, is that of relaxing the above constraint, while not fal...

Approximating automata are nite-state representations of the sequential input-output behaviors of hybrid systems characterized by threshold events that trigger discrete changes in the continuous dynamic equations. Procedures proposed for constructing approximating automata require forward and backward mappings of sets of continuous state trajectories { mappings which are not available for arbit...

We give new general methods for constructing small non-deterministic 4nite automata (NFA) from arbitrary ones. Given an NFA, we compute the largest right-invariant equivalence on the set of states and then merge the equivalent states to obtain a smaller automaton. When applying this method to position automata, we get a way to convert regular expressions into NFAs which are always smaller than ...

We study the dynamics of cellular automata, and more specifically their transitivity and expansivity, when the set of configurations is endowed with a shift-invariant (pseudo-)distance. We first give an original proof of the non-transitivity of cellular automata when the set of configurations is endowed with the Besicovitch pseudo-distance. We then show that the Besicovitch pseudo-distance indu...

Polyhedral analysis infers invariant linear equalities and inequalities of imperative programs. However, the exponential complexity of polyhedral operations such as image computation and convex hull limits the applicability of polyhedral analysis. Weakly relational domains such as intervals and octagons address the scalability issue by considering polyhedra whose constraints are drawn from a re...

We present a class of random cellular automata with multiple invariant measures which are all non-Gibbsian. The automata have configuration space {O,1f"d , with d > 1, and they are noisy versions of automata with the "eroder property". The noise is totally asymmetric in the sense that it allows random flippings of "0" into "1" but not the converse. We prove that all invariant measures assign to...

A hybrid system is a dynamical system reacting to continuous and discrete changes simultaneously. Many researchers have proposed modeling and verification formalisms for hybrid systems, but algorithmic verification of important properties such as safety and reachability is still an on-going research area. This paper demonstrates that a basic modeling formalism for hybrid systems, DEV&DESS is an...