Density classification on infinite lattices and trees
Identifieur interne : 001F97 ( Main/Exploration ); précédent : 001F96; suivant : 001F98Density classification on infinite lattices and trees
Auteurs : Ana Busic [France] ; Nazim Fatès [France] ; Jean Mairesse [France] ; Irène Marcovici [France]Source :
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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.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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</address>
<ref type="url">http://www.univ-paris-diderot.fr</ref>
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<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
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<country>France</country>
</affiliation>
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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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</address>
<ref type="url">http://www.liafa.jussieu.fr/</ref>
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<orgName type="acronym">UP7</orgName>
<desc><address><addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
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<ref type="url">http://www.univ-paris-diderot.fr</ref>
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</hal:affiliation>
<country>France</country>
</affiliation>
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<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Cellular automata</term>
<term>density classification</term>
<term>interacting particle systems</term>
<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>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Nancy</li>
</settlement>
<orgName><li>Institut national polytechnique de Lorraine</li>
<li>Université Nancy 2</li>
<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>
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