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Computation with perturbed dynamical systems

Abstract : This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability.
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Olivier Bournez, Daniel Graça, Emmanuel Hainry. Computation with perturbed dynamical systems. Journal of Computer and System Sciences, Elsevier, 2013, 79 (5), pp.714-724. ⟨10.1016/j.jcss.2013.01.025⟩. ⟨hal-00643634v2⟩

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