A comparative investigation into optimum-time synchronization protocols for a large scale of one dimensional cellular automata

Authors:
Hiroshi Umeo;Masaya Hisaoka;Takashi Sogabe
Affiliations:
Univ. of Osaka Electro-Communication, Neyagawa-shi, Osaka, Japan;Univ. of Osaka Electro-Communication, Neyagawa-shi, Osaka, Japan;Internet Initiative Japan Inc., Tokyo, Japan
Venue:
ISPA'03 Proceedings of the 2003 international conference on Parallel and distributed processing and applications
Year:
2003

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Abstract

The firing squad synchronization problem has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed. In the present paper, we examine the state transition rule sets for the famous firing squad synchronization algorithms that give a finite-state protocol for synchronizing large-scale cellular automata. We show that the first transition rule set designed by Waksman [18] includes fundamental errors which cause unsuccessful firings and that ninety-three percent of the rules are redundant. In addition, the transition rule sets reported by Balzer [1], Gerken [2] and Mazoyer [6] are found to include several redundant rules. We also present herein a survey and a comparison of the quantitative aspects of the optimumtime synchronization algorithms developed thus far for one-dimensional cellular arrays.