Density Classification on Infinite Lattices and Trees

Ana Busic 1, 2, 3 Nazim Fatès 4 Irène Marcovici 5 Jean Mairesse 5
3 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
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 metadatas

https://hal.inria.fr/hal-00918583
Contributor : Nazim Fatès <>
Submitted on : Friday, December 13, 2013 - 5:15:48 PM
Last modification on : Thursday, October 17, 2019 - 12:36:04 PM

Links full text

Identifiers

Citation

Ana Busic, 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⟩

Share

Metrics

Record views

560