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Classification of Finite Dynamical Systems

Luis Garcia·Abdul Salam Jarrah·Reinhard Laubenbacher
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Abstract

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by composing functions defined on the coordinates. The classification is in terms of the dependency relations among the coordinate functions. It suggests a natural notion of the linearization of a system. Furthermore, it contains a sharp upper bound on the number of systems in terms of the dependencies among the coordinate functions. This upper bound generalizes an upper bound for sequential dynamical systems.

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Luis Garcia, Abdul Salam Jarrah, Reinhard Laubenbacher. 2001-12-20. Classification of Finite Dynamical Systems. https://arxiv.org/abs/math/0112216

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