{"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/turing-machines-deciders-part-i","title":"Turing machines deciders, part I","arxiv_id":"2504.20563","date":"2025-04-29","proceeding":null,"authors":["The bbchallenge Collaboration","Justin Blanchard","Konrad Deka","Nathan Fenner","Tony Guilfoyle","Iijil","Maja Kądziołka","Pavel Kropitz","Shawn Ligocki","Pascal Michel","Mateusz Naściszewski","Tristan Stérin"],"abstract":"The Busy Beaver Challenge (or bbchallenge) aims at collaboratively solving the following conjecture: \"$S(5) = 47{,}176{,}870$\" [Rad\\'o, 1962], [Marxen and Buntrock, 1990], [Aaronson, 2020]. This conjecture says that if a 5-state Turing machine runs for more than 47,176,870 steps without halting, then it will never halt -- starting from the all-0 tape. Proving this conjecture amounts to deciding whether 181,385,789 Turing machines with 5 states halt or not -- starting from the all-0 tape [bbchallenge, 2025]. To do so, we write $\\textit{deciders}$: programs that take as input a Turing machine and output either HALT, NONHALT, or UNKNOWN. Each decider is specialised in recognising a particular type of non-halting behavior. After two years of work, the Busy Beaver Challenge achieved its goal in July 2024 by delivering a proof of \"$S(5) = 47{,}176{,}870$\" formalised in Coq [bbchallenge, 2025]. In this document, we present deciders that were developed before the Coq proof and which were mainly not used in the proof; nonetheless, they are relevant techniques for analysing Turing machines. Part II of this work is the decider section of our paper showing \"$S(5) = 47{,}176{,}870$\" [bbchallenge, 2025], presenting the deciders that were used in the Coq proof.","url_abs":"https://arxiv.org/abs/2504.20563v1","url_pdf":"https://arxiv.org/pdf/2504.20563v1.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":"turing-machines-deciders-part-i","repo_url":"https://github.com/Nathan-Fenner/bbchallenge-dafny-deciders","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}