Infinitely growing configurations in Emil Post's tag system problem
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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.
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