【摘要】 证明可加元胞自动器所有状态的进度都相同,所有的树结构都全同。如果演化矩阵中对应于奇异部分的初等因子的指数都相等,那么所有的枝长也全相等。近邻相互作用零边界条件可加元胞自动器具有上述性质。我们导出此类元胞自动器熵的解析公式。更多还原

【Abstract】 We demonstrate that, for an additive cellular automaton, the in-degrees of all states and the trees rooted at all nodes are identical, and all branches have same length if elementary divisors corresponding to singular part of the evolution matrix have same exponent. The one-dimensional additive cellular automata with a three-site neighborhood and null boundary conditions have all these properties, and we derive analytical formulae for such entropy of cellular automata更多还原