Two-dimensional traffic rules and the density classification problem
Identifieur interne : 000048 ( Main/Exploration ); précédent : 000047; suivant : 000049Two-dimensional traffic rules and the density classification problem
Auteurs : Nazim Fatès [France] ; Irène Marcovici [France] ; Siamak Taati [Pays-Bas]Source :
Abstract
The density classification problem is the computational problem of finding the majority in a given array of votes in a distributed fashion. It is known that no cellular automaton rule with binary alphabet can solve the density classification problem. On the other hand, it was shown that a probabilistic mixture of the traffic rule and the majority rule solves the one-dimensional problem correctly with a probability arbitrarily close to one. We investigate the possibility of a similar approach in two dimensions. We show that in two dimensions, the particle spacing problem, which is solved in one dimension by the traffic rule, has no cellular automaton solution. However, we propose exact and randomized solutions via interacting particle systems. We assess the performance of our models using numeric simulations.
Url:
Affiliations:
- France, Pays-Bas
- Grand Est, Lorraine (région)
- Metz, Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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It is known that no cellular automaton rule with binary alphabet can solve the density classification problem. On the other hand, it was shown that a probabilistic mixture of the traffic rule and the majority rule solves the one-dimensional problem correctly with a probability arbitrarily close to one. We investigate the possibility of a similar approach in two dimensions. We show that in two dimensions, the particle spacing problem, which is solved in one dimension by the traffic rule, has no cellular automaton solution. However, we propose exact and randomized solutions via interacting particle systems. We assess the performance of our models using numeric simulations.</div></front></TEI><affiliations><list><country><li>France</li><li>Pays-Bas</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><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"><region name="Grand Est"><name sortKey="Fates, Nazim" sort="Fates, Nazim" uniqKey="Fates N" first="Nazim" last="Fatès">Nazim Fatès</name></region><name sortKey="Marcovici, Irene" sort="Marcovici, Irene" uniqKey="Marcovici I" first="Irène" last="Marcovici">Irène Marcovici</name></country><country name="Pays-Bas"><noRegion><name sortKey="Taati, Siamak" sort="Taati, Siamak" uniqKey="Taati S" first="Siamak" last="Taati">Siamak Taati</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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