A new optimum-time firing squad synchronization algorithm for two-dimensional rectangle arrays: one-sided recursive halving based

Authors:
H. Umeo;K. Nishide;T. Yamawaki
Affiliations:
Osaka Electro-Communication University, Neyagawa-shi, Osaka, Japan;Osaka Electro-Communication University, Neyagawa-shi, Osaka, Japan;Osaka Electro-Communication University, Neyagawa-shi, Osaka, Japan
Venue:
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Year:
2011

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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 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.