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引用次数: 0
摘要
可逆性是细胞自动机(CA)最重要的特性之一。本文重点研究一维有限 CA 在反射边界条件(RBC)下的可逆性。我们提出了两种在 RBC 条件下判定一维有限 CA 可逆性的算法。这两种算法不仅适用于线性规则,也适用于非线性规则。第一种算法是确定 CA 的 "严格可逆性"。第二种算法是计算 CA 的 "可逆函数"。可逆函数被证明是周期性的。根据这些算法,我们列出了 RBC 下一维 CA 的一些实验结果,并分析了该系列 CA 的一些特点。
Decision algorithms for reversibility of 1D cellular automata under reflective boundary conditions
Reversibility is one of the most significant properties of cellular automata (CA). In this paper, we focus on the reversibility of one-dimensional finite CA under reflective boundary conditions (RBC). We present two algorithms for deciding the reversibility of one-dimensional CA under RBC. Both algorithms work for not only linear rules but also non-linear rules. The first algorithm is to determine what we call the “strict reversibility” of CA. The second algorithm is to compute what we call the “reversibility function” of CA. Reversibility functions are proved to be periodic. Based on the algorithms, we list some experiment results of one-dimensional CA under RBC and analyse some features of this family of CA.
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.