Emil Post's tag system problem is 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. For the past decades, there were several attempts to find an answer to this question, including a recent study by Wolfram (2021), during which the first $2^{84}$ initial configurations were checked. This paper presents a family of configurations of this type in a form of strings $a^{n} b c^{m}$, that evolve to $a^{n+1} b c^{m+1}$ after a finite amount of steps. The proof of this behavior for all non-negative $n$ and $m$ is described further in a paper as a finite verification procedure, which is computationally bounded by 20000 iterations of tag. All corresponding code can be found at https://github.com/nikitakurilenko/post-tag-infinitely-growing-configurations.

中文翻译：

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Emil Post的标签系统问题中无限增长的配置

Emil Post的标签系统问题是标签系统$ \ {N = 3，P（0）= 00，P（1）= 1101 \} $是否具有配置，模拟不会停止或结束的问题循环上升。在过去的几十年中，进行了多次尝试来找到这个问题的答案，包括Wolfram（2021）的最近一项研究，在该研究中，检查了最初的$ 2 ^ {84} $初始配置。本文以字符串$ a ^ {n} bc ^ {m} $的形式介绍了这种类型的配置，经过有限的处理后演变为$ a ^ {n + 1} bc ^ {m + 1} $步数。所有非负$ n $和$ m $的这种行为的证明在论文中进一步描述为有限验证程序，该程序在计算上受标记的20000次迭代的限制。所有相应的代码都可以在https://github.com/nikitakurilenko/post-tag-infinitely-growing-configurations中找到。