Density classification on infinite lattices and trees
Probability
2011-11-22 v1 Discrete Mathematics
Cellular Automata and Lattice Gases
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.
Cite
@article{arxiv.1111.4582,
title = {Density classification on infinite lattices and trees},
author = {Ana Busic and Nazim Fates and Jean Mairesse and Irene Marcovici},
journal= {arXiv preprint arXiv:1111.4582},
year = {2011}
}