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- W2571307280 abstract "Consider an infinite graph with nodes initially labeled by independent Bernoullirandom 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." @default.
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- W2571307280 date "2013-01-01" @default.
- W2571307280 modified "2023-10-17" @default.
- W2571307280 title "Density classification on infinite lattices and trees" @default.
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- W2571307280 doi "https://doi.org/10.1214/ejp.v18-2325" @default.
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