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arXiv · 2105.07529

Infinitely growing configurations in Emil Post's tag system problem

Nikita V. Kurilenko
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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 20 000 iterations of tag.

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Nikita V. Kurilenko. 2021-05-16. Infinitely growing configurations in Emil Post's tag system problem. https://doi.org/10.25088/complexsystems.31.3.279

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