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Probabilistic Cellular AutomataAn Example of Computation of the Density of Ones in Probabilistic Cellular Automata by Direct Recursion

Probabilistic Cellular Automata: An Example of Computation of the Density of Ones in... [We present a method for computing probability of occurrence of ones in a configuration obtained by iteration of a probabilistic cellular automata (PCA), starting from a random initial configuration. If the PCA is sufficiently simple, one can construct a set of words (or blocks of symbols) which is complete, meaning that probabilities of occurrence of words from this set can be expressed as linear combinations of probabilities of occurrence of these words at the previous time step. One can then set up and solve a recursion for block probabilities. We demonstrate an example of such PCA, which can be viewed as a simple model of diffusion of information or spread of rumours. Expressions for the density of ones are obtained for this rule using the proposed method.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Probabilistic Cellular AutomataAn Example of Computation of the Density of Ones in Probabilistic Cellular Automata by Direct Recursion

Part of the Emergence, Complexity and Computation Book Series (volume 27)
Editors: Louis, Pierre-Yves; Nardi, Francesca R.
Fukś, Henryk
Probabilistic Cellular Automata — Feb 22, 2018
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13 pages

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG 2018
ISBN
978-3-319-65556-7
Pages
131 –144
DOI
10.1007/978-3-319-65558-1_10
Publisher site
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Abstract

[We present a method for computing probability of occurrence of ones in a configuration obtained by iteration of a probabilistic cellular automata (PCA), starting from a random initial configuration. If the PCA is sufficiently simple, one can construct a set of words (or blocks of symbols) which is complete, meaning that probabilities of occurrence of words from this set can be expressed as linear combinations of probabilities of occurrence of these words at the previous time step. One can then set up and solve a recursion for block probabilities. We demonstrate an example of such PCA, which can be viewed as a simple model of diffusion of information or spread of rumours. Expressions for the density of ones are obtained for this rule using the proposed method.]

Published: Feb 22, 2018

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