InforLorV4, Main, Exploration, bibRecord, 001375

Density Classification on Infinite Lattices and Trees

Identifieur interne : 001375 ( Main/Exploration ); précédent : 001374; suivant : 001376

Density Classification on Infinite Lattices and Trees

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

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

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 001B52
to stream Hal, to step Curation: 001B52
to stream Hal, to step Checkpoint: 001345
to stream Main, to step Merge: 001388
to stream Main, to step Curation: 001375

Le document en format XML

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<tutelles><tutelle active="#struct-300301" type="direct"><org type="institution" xml:id="struct-300301" status="VALID"><orgName>Université Paris Diderot - Paris 7</orgName>
<orgName type="acronym">UP7</orgName>
<desc><address><addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-paris-diderot.fr</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7089" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1214/EJP.v18-2325</idno>
<series><title level="j">Electronic Journal of Probability</title>
<idno type="ISSN">1083-6489</idno>
<imprint><date type="datePub">2013</date>
</imprint>
</series>
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</fileDesc>
<profileDesc><textClass></textClass>
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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>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="France"><noRegion><name sortKey="Busic, Ana" sort="Busic, Ana" uniqKey="Busic A" first="Ana" last="Busic">Ana Busic</name>
</noRegion>
<name sortKey="Fates, Nazim" sort="Fates, Nazim" uniqKey="Fates N" first="Nazim" last="Fatès">Nazim Fatès</name>
<name sortKey="Mairesse, Jean" sort="Mairesse, Jean" uniqKey="Mairesse J" first="Jean" last="Mairesse">Jean Mairesse</name>
<name sortKey="Marcovici, Irene" sort="Marcovici, Irene" uniqKey="Marcovici I" first="Irène" last="Marcovici">Irène Marcovici</name>
</country>
</tree>
</affiliations>
</record>

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Density Classification on Infinite Lattices and Trees

Density Classification on Infinite Lattices and Trees

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