Max-plus analysis on some binary particle systems
Daisuke A. Takahashi, Junta Matsukidaira, Hiroaki Hara, Bao‐Feng Feng · Journal of Physics A Mathematical and Theoretical · 2011
We are concerned with a special class of binary cellular automata, i.e. the so-called particle cellular automata (PCA) in this paper. We first propose max-plus expressions to PCA of four 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.