{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:41:13Z","timestamp":1753890073103,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T00:00:00Z","timestamp":1587686400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T00:00:00Z","timestamp":1587686400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T00:00:00Z","timestamp":1587686400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["794020"],"award-info":[{"award-number":["794020"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>Infinite time Turing machine models with tape length $\\alpha$, denoted $T_\\alpha$, strengthen the machines of Hamkins and Kidder [HL00] with tape length $\\omega$. A new phenomenon is that for some countable ordinals $\\alpha$, some cells cannot be halting positions of $T_\\alpha$ given trivial input. The main open question in [Rin14] asks about the size of the least such ordinal $\\delta$.   We answer this by providing various characterizations. For instance, $\\delta$ is the least ordinal with any of the following properties: (a) For some $\\xi&amp;lt;\\alpha$, there is a $T_\\xi$-writable but not $T_\\alpha$-writable subset of $\\omega$. (b) There is a gap in the $T_\\alpha$-writable ordinals. (c) $\\alpha$ is uncountable in $L_{\\lambda_\\alpha}$. Here $\\lambda_\\alpha$ denotes the supremum of $T_\\alpha$-writable ordinals, i.e. those with a $T_\\alpha$-writable code of length $\\alpha$.   We further use the above characterizations, and an analogue to Welch's submodel characterization of the ordinals $\\lambda$, $\\zeta$ and $\\Sigma$, to show that $\\delta$ is large in the sense that it is a closure point of the function $\\alpha \\mapsto \\Sigma_\\alpha$, where $\\Sigma_\\alpha$ denotes the supremum of the $T_\\alpha$-accidentally writable ordinals.<\/jats:p>","DOI":"10.23638\/lmcs-16(2:2)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:31Z","timestamp":1743701851000},"source":"Crossref","is-referenced-by-count":0,"title":["Reachability for infinite time Turing machines with long tapes"],"prefix":"10.23638","volume":"Volume 16, Issue 2","author":[{"given":"Merlin","family":"Carl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin","family":"Rin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7736-7466","authenticated-orcid":false,"given":"Philipp","family":"Schlicht","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2020,4,24]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1802.05734v10","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1802.05734v10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:31Z","timestamp":1743701851000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,24]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(2:2)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1802.05734v8","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.05734v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.05734v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.05734v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.05734v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1802.05734","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1802.05734","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2020,4,24]]},"article-number":"4444"}}