InforLorV4, Main, Curation, bibRecord, 001F97

Density classification on infinite lattices and trees

Identifieur interne : 001F97 ( Main/Curation ); précédent : 001F96; suivant : 001F98

Density classification on infinite lattices and trees

Auteurs : Ana Busic [France] ; Nazim Fatès [France] ; Jean Mairesse [France] ; Irène Marcovici [France]

Source :

RBID : Hal:hal-00643468

English descriptors

mix :
- Cellular automata, density classification, interacting particle systems, percolation, percolation..

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 that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations.

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https://hal.archives-ouvertes.fr/hal-00643468

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<country>France</country>
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<author><name sortKey="Marcovici, Irene" sort="Marcovici, Irene" uniqKey="Marcovici I" first="Irène" last="Marcovici">Irène Marcovici</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-1033" status="OLD"><orgName>Laboratoire d'informatique Algorithmique : Fondements et Applications</orgName>
<orgName type="acronym">LIAFA</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>Université Paris Diderot, Bât. Sophie Germain, case postale 7014, 75205 Paris cedex 13</addrLine>
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<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Cellular automata</term>
<term>density classification</term>
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<term>percolation</term>
<term>percolation.</term>
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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 that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations.</div>
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Density classification on infinite lattices and trees

Density classification on infinite lattices and trees

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