{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/infinitely-growing-configurations-in-emil","title":"Infinitely growing configurations in Emil Post's tag system problem","arxiv_id":"2105.07529","date":"2021-05-16","proceeding":null,"authors":["Nikita V. Kurilenko"],"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.","url_abs":"https://arxiv.org/abs/2105.07529v2","url_pdf":"https://arxiv.org/pdf/2105.07529v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"infinitely-growing-configurations-in-emil","repo_url":"https://github.com/nikitakurilenko/post-tag-infinitely-growing-configurations","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}