{"paper":{"title":"Ultimate periodicity of b-recognisable sets : a quasilinear procedure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Jacques Sakarovitch, Victor Marsault","submitted_at":"2013-01-12T15:07:25Z","abstract_excerpt":"It is decidable if a set of numbers, whose representation in a base b is a regular language, is ultimately periodic. This was established by Honkala in 1986.\n  We give here a structural description of minimal automata that accept an ultimately periodic set of numbers. We then show that it can verified in linear time if a given minimal automaton meets this description.\n  This thus yields a O(n log(n)) procedure for deciding whether a general deterministic automaton accepts an ultimately periodic set of numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2691","kind":"arxiv","version":2},"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"}