Algorithmic analysis of irrational rotations in a single neuron model

Authors:
Hayato Takahashi;Kazuyuki Aihara
Affiliations:
The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan;Department of Mathematical Engineering and Information Physics, Graduate School of Engineering, University of Tokyo, and CREST, Japan Science and Technology Corporation (JST), Saitama 332-0012, Ja ...
Venue:
Journal of Complexity
Year:
2003

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Abstract

We study computability of real-valued functions and the information needed for simulation of dynamical systems. In particular, we describe application of Kolmogorov complexity theory to computer simulation of irrational rotations in a single neuron model. We deduce the information needed for a parameter in simulating the dynamics by showing a difference in Kolmogorov complexity between a computable parameter and a non-computable parameter. Finally, we show that all trajectories generated by irrational rotations are non-computable iff its parameter is non-computable.