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Published in:
2010 | OriginalPaper | Chapter
A Seven-State Time-Optimum Square Synchronizer
Authors : Hiroshi Umeo, Keisuke Kubo
Published in: Cellular Automata
Publisher: Springer Berlin Heidelberg
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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 seven-state optimum-time synchronization algorithm that can synchronize any square arrays of size
n
×
n
with a general at one corner in 2
n
− 2 steps, which is a smallest realization of time-optimum square synchronizer known at present. The implementation is based on a new, simple zebra-like mapping scheme which embeds synchronization operations on one-dimensional arrays onto square arrays.