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Classification of Elementary Cellular Automata Up to Topological Conjugacy
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21st IFIP WG 1.5 International Workshop, AUTOMATA 2015
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Turku, Finland,
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Topological conjugacy is the natural notion of isomorphism in topological dynamics. It can be used as a very fine grained classification scheme for cellular automata. In this article, we investigate different invariants for topological conjugacy in order to distinguish between non-conjugate systems. In particular we show how to compute the cardinality of the set of points with minimal period n for one-dimensional CA. Applying these methods to the 256 elementary one-dimensional CA, we show that up to topological conjugacy there are exactly 83 of them.
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