{"paper":{"title":"Some Observations on Infinitary Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Merlin Carl","submitted_at":"2018-01-30T14:59:04Z","abstract_excerpt":"Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\\\"owe and the author, we prove the following results:\n  (1) An analogue of Ladner's theorem for OTMs holds: That is, there are languages $\\mathcal{L}$ which are NP$^{\\infty}$, but neither P$^{\\infty}$ nor NP$^{\\infty}$-complete. This answers an open question of \\cite{CLR}.\n  (2) The speedup theorem for Turing machines, which allows us to bring down the computation time and space usage of a Turing machine program down by an aribtrary positive factor under relatively mild side condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}