A seven-state time-optimum square synchronizer

Authors:
Hiroshi Umeo;Keisuke Kubo
Affiliations:
Univ. of Osaka Electro-Communication, Neyagawa-shi, Osaka, Japan;Univ. of Osaka Electro-Communication, Neyagawa-shi, Osaka, Japan
Venue:
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Year:
2010

Citing 6
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Abstract

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 2n - 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.