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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2011

Orbits of the Bernoulli measure in single-transition asynchronous cellular automata

Résumé

We study iterations of the Bernoulli measure under nearest-neighbour asynchronous binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicitly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions for probabilities of ones for all three minimal single-transition rules, as well as expressions for probabilities of blocks of length 3 for some of them. These expressions can be interpreted as "response curves'', that is, curves describing the dependence of the final density of ones on the initial density of ones.
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Dates et versions

hal-01196139 , version 1 (09-09-2015)

Identifiants

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Henryk Fukś, Andrew Skelton. Orbits of the Bernoulli measure in single-transition asynchronous cellular automata. 17th International Workshop on Celular Automata and Discrete Complex Systems, 2011, Santiago, Chile. pp.95-112, ⟨10.46298/dmtcs.2972⟩. ⟨hal-01196139⟩

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