Skip to Main content Skip to Navigation
Journal articles

Density Classification on Infinite Lattices and Trees

Ana Bušić 1, 2, 3 Nazim Fatès 4 Irène Marcovici 5 Jean Mairesse 5
3 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
4 MAIA - Autonomous intelligent machine
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
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.
Complete list of metadata
Contributor : Nazim Fatès Connect in order to contact the contributor
Submitted on : Friday, December 13, 2013 - 5:15:48 PM
Last modification on : Saturday, October 16, 2021 - 11:26:07 AM

Links full text



Ana Bušić, Nazim Fatès, Irène Marcovici, Jean Mairesse. Density Classification on Infinite Lattices and Trees. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18 (51), pp.1-22. ⟨10.1214/EJP.v18-2325⟩. ⟨hal-00918583⟩



Record views