Computability properties of low-dimensional dynamical systems

  • Michel Cosnard
  • Max Garzon
  • Pascal Koiran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

It has been known for a short time that a class of recurrent neural networks has universal computational abilities. These networks can be viewed as iterated piecewise-linear maps in a high-dimensional space. In this paper, we show that similar systems in dimension two are also capable of universal computations. On the contrary, it is necessary to resort to more complex systems (e.g., iterated piecewise-monotone maps) in order to retain this capability in dimension one.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Michel Cosnard
    • 1
  • Max Garzon
    • 1
  • Pascal Koiran
    • 1
  1. 1.Unité de Recherche Associée 1398 du CNRS Ecole Normale Supérieure de LyonLIP-IMAGLyon Cedex 07France

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