Asynchronous cellular system that solves the parity problem
Résumé
We present stochastic cellular automata that classify the parity of
initial conditions. The model is an interacting particles system where
cells are updated by pairs, randomly chosen at each time step. A first
rule is proposed, with a symmetry between 0's and 1's. We show that
it classifies the parity of the initial configurations thanks to a non-biased random walk of the frontiers between 0's and 1's. We present an analysis of the classification time, as well as numerical simulations, to establish that the classification time scales quadratically with the number of cells. In a second time, breaking the state symmetry, we propose an improvement of this rule with the simultaneous use of two classifying systems.
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