Orbits of the Bernoulli measure in single-transition asynchronous cellular automata - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2011

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

Abstract

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.
Fichier principal
Vignette du fichier
dmAP0107.pdf (405.38 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

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

Identifiers

Cite

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⟩

Collections

INSMI TDS-MACS
91 View
592 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More