Open Access
2013 Density classification on infinite lattices and trees
Ana Bušić, Nazim Fatès, Jean Mairesse, Irène Marcovici
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Electron. J. Probab. 18: 1-22 (2013). DOI: 10.1214/EJP.v18-2325


Consider an infinite graph with nodes initially labeled by independent Bernoullirandom 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.


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Ana Bušić. Nazim Fatès. Jean Mairesse. Irène Marcovici. "Density classification on infinite lattices and trees." Electron. J. Probab. 18 1 - 22, 2013.


Accepted: 24 April 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1288.60125
MathSciNet: MR3048123
Digital Object Identifier: 10.1214/EJP.v18-2325

Primary: 60K35 , 68Q80
Secondary: 37B15 , 60J05

Keywords: cellular automata , density classification , interacting particle systems

Vol.18 • 2013
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