Synchronizing Two-Dimensional Cellular Automata in Optimum-Time

概要

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The firing squad synchronization problem on cellular automata has been studied extensively for more than fifty years, and a rich variety of synchronization algorithms have been proposed for not only one-dimensional arrays but two-dimensional arrays. In the present paper, we propose a new optimum-time synchronization algorithm that can synchronize any two-dimensional rectangle arrays of size m × n with a general at one corner in m + n + max(m, n) - 3 steps. The algorithm is based on a simple recursive halving marking schema which helps synchronization operations on two-dimensional arrays. A proposed computer-assisted implementation of the algorithm gives a description of a two-dimensional cellular automaton in terms of a finite 384-state set and a local 112690-rule set.
2011-05-09