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Neural Networks and Computational Learning Theory

 

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NeuroCOLT Technical Report NC-TR-96-005

On the computational power and super-Turing capabilities of dynamical systems

Olivier Bournez
Department LIP
ENS-Lyon
France

Michel Cosnard
Department LIP
ENS-Lyon
France

Abstract
We explore the simulation and computational capabilities of dynamical systems. We first introduce and compare several notions of simulation between discrete systems. We give a general framework that allows dynamical systems to be considered as computational machines. We introduce a new discrete model of computation: the analog automaton model. We determine the computational power of this model and prove that it does have super-Turing capabilities. We then prove that many very simple dynamical systems from the literature are actually able to simulate analog automata. From this result we deduce that many   dynamical systems have intrinsically super-Turing capabilities.

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