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Entropy 2003, 5(2), 233-238; doi:10.3390/e5020233
Article

On the Measure Entropy of Additive Cellular Automata f

Arts and Sciences Faculty, Department of Mathematics, Harran University; 63100, Şanlıurfa, Turkey
Received: 5 February 2003 / Accepted: 12 June 2003 / Published: 30 June 2003
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Abstract

We show that for an additive one-dimensional cellular automata f on space of all doubly infinitive sequences with values in a finite set S = {0, 1, 2, ..., r-1}, determined by an additive automaton rule [equation] (mod r), and a f-invariant uniform Bernoulli measure μ, the measure-theoretic entropy of the additive one-dimensional cellular automata f with respect to μ is equal to hμ (f) = 2klog r, where k ≥ 1, r-1∈S. We also show that the uniform Bernoulli measure is a measure of maximal entropy for additive one-dimensional cellular automata f.
Keywords: Cellular Automata; Measure Entropy; Topological Entropy Cellular Automata; Measure Entropy; Topological Entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Akın, H. On the Measure Entropy of Additive Cellular Automata f. Entropy 2003, 5, 233-238.

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