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.
This work was partially supported by the Programme de Recherches Coordonnées C3 of the CNRS and the Ministère de la Recherche et de la Technologie.
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© 1993 Springer-Verlag Berlin Heidelberg
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Cosnard, M., Garzon, M., Koiran, P. (1993). Computability properties of low-dimensional dynamical systems. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_37
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DOI: https://doi.org/10.1007/3-540-56503-5_37
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