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arXiv · 1012.4887

Max-plus analysis on some binary particle systems

Daisuke Takahashi·Junta Matsukidaira·Hiroaki Hara·Bao-Feng Feng
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Abstract

We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.

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Daisuke Takahashi, Junta Matsukidaira, Hiroaki Hara, Bao-Feng Feng. 2010-12-22. Max-plus analysis on some binary particle systems. https://doi.org/10.1088/1751-8113/44/13/135102

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