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 [1], [2] and [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.
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Umeo, H., Hisaoka, M., Sogabe, T. (2003). A Comparative Investigation into Optimum-Time Synchronization Protocols for a Large Scale of One-Dimensional Cellular Automata. In: Guo, M., Yang, L.T. (eds) Parallel and Distributed Processing and Applications. ISPA 2003. Lecture Notes in Computer Science, vol 2745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37619-4_18
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DOI: https://doi.org/10.1007/3-540-37619-4_18
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