没有六单元邻域蜂窝自动机能解决奇偶性问题

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2024-10-28 DOI:10.1016/j.tcs.2024.114923

Anna Nenca , Barbara Wolnik , Bernard De Baets

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引用次数: 0

摘要

奇偶性问题是研究细胞自动机计算能力的最著名分类问题之一。在这一逆向问题中，我们要寻找一种能根据奇偶性将每个初始配置分为两类的蜂窝自动机。在确定性一维蜂窝自动机中，存在一种能有效解决奇偶性问题的局部规则，但它是否是可能的最简单规则还不得而知。具体地说，我们知道具有九个单元邻域的细胞自动机可以解决奇偶性问题，而具有五个单元邻域的细胞自动机却不能解决奇偶性问题。这些发现在过去 10 年中一直没有得到改进。在本文中，我们提出了缩小现有差距的新工具。在这些工具的帮助下，我们能够证明不存在具有六单元邻域的细胞自动机能够解决奇偶性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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No six-cell neighborhood cellular automaton solves the parity problem

The parity problem is one of the best-known classification problems studied to examine the computational abilities of cellular automata. In this inverse problem, one is looking for a cellular automaton that can classify each initial configuration into one of two classes according to its parity. In the case of deterministic one-dimensional cellular automata, there exists a local rule that effectively solves the parity problem, but it is unknown whether it is the simplest possible rule. Specifically, it is known that a cellular automaton with a nine-cell neighborhood can solve the parity problem, whereas no cellular automaton with a five-cell neighborhood is capable of doing so. These findings have remained unimproved for the past 10 years. In this paper, we present novel tools that allow to narrow down the existing gap. With the help of these tools, we are able to demonstrate that there is no cellular automaton with a six-cell neighborhood capable of solving the parity problem.

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

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.