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arXiv · 1208.2761

A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata

Hiroshi Umeo·Kinuo Nishide·Keisuke Kubo
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Abstract

The firing squad synchronization problem (FSSP) on cellular automata has been studied extensively for more than forty 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 simple recursive-halving based optimum-time synchronization algorithm that can synchronize any rectangle arrays of size m*n with a general at one corner in m+n+max(m, n)-3 steps. The algorithm is a natural expansion of the well-known FSSP algorithm proposed by Balzer [1967], Gerken [1987], and Waksman [1966] and it can be easily expanded to three-dimensional arrays, even to multi-dimensional arrays with a general at any position of the array.

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Hiroshi Umeo, Kinuo Nishide, Keisuke Kubo. 2012-08-14. A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata. https://doi.org/10.4204/eptcs.90.13

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