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arXiv · 1111.4582

Density classification on infinite lattices and trees

Ana Busic·Nazim Fates·Jean Mairesse·Irene Marcovici
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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.

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Ana Busic, Nazim Fates, Jean Mairesse, Irene Marcovici. 2011-11-19. Density classification on infinite lattices and trees. https://arxiv.org/abs/1111.4582

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