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.
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Umeo, H., Nishide, K., Yamawaki, T. (2011). A New Optimum-Time Firing Squad Synchronization Algorithm for Two-Dimensional Rectangle Arrays: One-Sided Recursive Halving Based. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_31
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DOI: https://doi.org/10.1007/978-3-642-21875-0_31
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