Synchronisation of Elementary Cellular Automata with a Small Initial Error. Application to Rule 18
Résumé
In this paper, we study how synchronization and state estimation are related in the context of elementary cellular automata. We first characterize the synchronization error between two 1D elementary cellular automata implementing Wolfram’s 18th rule. Then we propose a simple approach to statistically model the transient phase of the synchronization error spread. We finally present a way to utilize this model of the error spread to place mobile sensors in order to reduce the overall synchronization error when the initial error is small.
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