{"paper":{"title":"The Degree of Squares is an Atom (Extended Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Clemens Grabmayer, Dimitri Hendriks, Hans Zantema, J\\\"org Endrullis","submitted_at":"2015-06-02T13:52:22Z","abstract_excerpt":"We answer an open question in the theory of degrees of infinite sequences with respect to transducibility by finite-state transducers. An initial study of this partial order of degrees was carried out in (Endrullis, Hendriks, Klop, 2011), but many basic questions remain unanswered. One of the central questions concerns the existence of atom degrees, other than the degree of the `identity sequence' 1 0^0 1 0^1 1 0^2 1 0^3 .... A degree is called an `atom' if below it there is only the bottom degree 0, which consists of the ultimately periodic sequences. We show that also the degree of the `squa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00884","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"}