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by Eugene Asarin, Ahmed Bouajjani
In Proceedings of the Sixteenth Annual IEEE Symposium on Logic in Computer Science. IEEE
http://www.liafa.jussieu.fr/~abou/Papers/asa-bou-lics01.ps.gz
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Abstract:
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 notion of perturbed dynamics by a small " (w.r.t. to a suitable metrics), and define the perturbed reachability relation as the intersection of all reachability relations obtained by "-perturbations, for all possible values of ". We show that for the four kinds of models we consider, the perturbed reachability relation is co-recursively enumerable, and that any co-r.e. relation can be defined as the perturbed reachability relation of such models. A corollary of this result is that systems that are robust, i.e., their reachability relation is stable under infinitesimal perturbation, are decidable.
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