Infinitely growing configurations in Emil Post's tag system problem

IF 0.7 4区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Advances in Complex Systems Pub Date : 2021-05-16 DOI:10.25088/ComplexSystems.31.3.279

N. Kurilenko

引用次数: 0

Abstract

Emil Post’s tag system problem posed the question of whether or not a tag system {N=3, P(0)=00, P(1)=1101} has a configuration, simulation of which will never halt or end up in a loop. Over the subsequent decades, there were several attempts to find an answer to this question, including a recent study, during which the first 2 84 initial configurations were checked. This paper presents a family of configurations of this type in the form of strings A n ⁢ B ⁢ C m that evolve to A n + 1 ⁢ B ⁢ C m + 1 after a finite number of steps. The proof of this behavior for all non-negative n and m is described later in this paper as a finite verification procedure, which is computationally bounded by 20000 iterations of tag.

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Emil Post标签系统问题中的无限增长结构

Emil Post的标签系统问题提出了一个问题，即标签系统{N=3, P(0)=00, P(1)=1101}是否有一个配置，其模拟永远不会停止或结束在一个循环中。在随后的几十年里，有几次试图找到这个问题的答案，包括最近的一项研究，在此期间检查了前284个初始配置。本文给出了这类构型的一个族，其形式为字符串a n减去B减去C m，经过有限的步数，它演化为a n + 1减去B减去C m + 1。对于所有非负n和非负m的这种行为的证明，本文稍后将描述为一个有限的验证过程，计算上以20000次迭代的标签为界。

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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来源期刊

Advances in Complex Systems 综合性期刊-数学跨学科应用

CiteScore

1.40

自引率

0.00%

发文量

121

审稿时长

6-12 weeks

期刊介绍： Advances in Complex Systems aims to provide a unique medium of communication for multidisciplinary approaches, either empirical or theoretical, to the study of complex systems. The latter are seen as systems comprised of multiple interacting components, or agents. Nonlinear feedback processes, stochastic influences, specific conditions for the supply of energy, matter, or information may lead to the emergence of new system qualities on the macroscopic scale that cannot be reduced to the dynamics of the agents. Quantitative approaches to the dynamics of complex systems have to consider a broad range of concepts, from analytical tools, statistical methods and computer simulations to distributed problem solving, learning and adaptation. This is an interdisciplinary enterprise.