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引用次数: 0
摘要
在本文中，我们完全解决了一维无限蜂窝自动机（FCA）的可逆性问题。这意味着我们将有一种有效的方法来确定任何具有所有单元数（n）的 FCA 的可逆性。我们在两种新图形上进行了计算，发现任何 FCA 的可逆性都会随着 n 的增加而呈现周期性。我们成功地提供了一种计算可逆性序列的方法，该序列包含任何单元数的 FCA 的可逆性。此外，本文的计算还适用于具有各种边界的 FCA。
The Computation for Reversibility of Arbitrary One-dimensional Finite Cellular Automata Becomes Efficient
In this paper, we completely solve the reversibility of one-dimensional
finite cellular automata (FCA). This means that we will have an efficient
method to determine the reversibility of any FCA with all numbers (n) of cells.
The complexity of this algorithm is independent of n. We perform calculations
on two new kinds of graphs and discover that the reversibility of any FCA
exhibits periodicity as n increases. We successfully provide a method to
compute the reversibility sequence that encompasses the reversibility of FCA
with any number of cells. Additionally, the calculations in this paper are
applicable to FCA with various types of boundaries.
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