两张图：解决一维有限元胞自动机的周期性可逆性问题
Two Graphs: Resolving the Periodic Reversibility of One-dimensional Finite Cellular Automata
AI总结：
本研究针对一维有限元胞自动机可逆性研究不足的问题，通过两张图的计算发现其可逆性随元胞数增加呈周期性，提出了可计算任意元胞数、适配多类边界的可逆性序列方法，实现了复杂度与元胞数无关的高效可逆性判定。
摘要：
有限元胞自动机（FCA）被广泛应用于非线性复杂系统的模拟，其可逆性与演化过程中的信息损失密切相关。然而，目前仅有相对较少的可逆性问题得到解决。本文通过对两张图进行计算，发现任意一维FCA的可逆性会随着元胞数量的增加呈现周期性特征。我们还成功提出了一种计算可逆性序列的方法，该序列涵盖了任意元胞数量的一维FCA的可逆性。此外，本文的计算方法适用于具有多种边界类型的FCA。这意味着我们将拥有一种高效的方法来判定几乎所有一维FCA的可逆性，其复杂度与元胞数量无关。
英文摘要：
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility problems has been solved. In this paper, we perform calculations on two graphs and discover that the reversibility of any one-dimensional FCA exhibits periodicity as the number of cells increases. We also successfully provide a method to compute the reversibility sequence that encompasses the reversibility of one-dimensional FCA with any number of cells. Additionally, the calculations in this paper are applicable to FCA with various types of boundaries. This means that we will have an efficient method to determine the reversibility of almost all one-dimensional FCA, with a complexity independent of cell number.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
