InforLorV4, Hal, Corpus, bibRecord, 001B52

Density Classification on Infinite Lattices and Trees

Identifieur interne : 001B52 ( Hal/Corpus ); précédent : 001B51; suivant : 001B53

Density Classification on Infinite Lattices and Trees

Auteurs : Ana Busic ; Nazim Fatès ; Irène Marcovici ; Jean Mairesse

Source :

Electronic Journal of Probability [ 1083-6489 ] ; 2013.

RBID : Hal:hal-00918583

Abstract

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic)cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p<1/2, and only 1's if p>1/2. We present solutions to the problem on the regular grids of dimension d, for any d>1, and on the regular infinite trees. For the bi-infinite line, we propose some candidates that we back up with numerical simulations.

Url:

https://hal.inria.fr/hal-00918583

DOI: 10.1214/EJP.v18-2325

Links to Exploration step

Hal:hal-00918583

Le document en format XML

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<front><div type="abstract" xml:lang="en">Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic)cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p<1/2, and only 1's if p>1/2. We present solutions to the problem on the regular grids of dimension d, for any d>1, and on the regular infinite trees. For the bi-infinite line, we propose some candidates that we back up with numerical simulations.</div>
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<author role="aut"><persName><forename type="first">Jean</forename>
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<abstract xml:lang="en">Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic)cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p<1/2, and only 1's if p>1/2. We present solutions to the problem on the regular grids of dimension d, for any d>1, and on the regular infinite trees. For the bi-infinite line, we propose some candidates that we back up with numerical simulations.</abstract>
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Density Classification on Infinite Lattices and Trees

Density Classification on Infinite Lattices and Trees

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