Papers › Infinitely growing configurations in Emil Post's tag system problem
Infinitely growing configurations in Emil Post's tag system problem
Nikita V. Kurilenko
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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 2⁸⁴ initial configurations were checked. This paper presents a family of configurations of this type in the form of strings Aⁿ B Cᵐ that evolve to Aⁿ⁺¹ B Cᵐ⁺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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