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.
Type de document :
Communication dans un congrès
Fatès, Nazim and Goles, Eric and Maass, Alejandro and Rapaport, Iván. 17th International Workshop on Celular Automata and Discrete Complex Systems, 2011, Santiago, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, pp.95-112, 2011, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01196139
Contributeur : Coordination Episciences Iam <>
Soumis le : mercredi 9 septembre 2015 - 11:14:59
Dernière modification le : mardi 7 mars 2017 - 15:18:03
Document(s) archivé(s) le : lundi 28 décembre 2015 - 23:01:41

Fichier

dmAP0107.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01196139, version 1

Collections

Citation

Henryk Fukś, Andrew Skelton. Orbits of the Bernoulli measure in single-transition asynchronous cellular automata. Fatès, Nazim and Goles, Eric and Maass, Alejandro and Rapaport, Iván. 17th International Workshop on Celular Automata and Discrete Complex Systems, 2011, Santiago, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, pp.95-112, 2011, DMTCS Proceedings. 〈hal-01196139〉

Partager

Métriques

Consultations de la notice

222

Téléchargements de fichiers

264