{"paper":{"title":"An efficient algorithm to decide periodicity of b-recognisable sets using MSDF convention","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.FL","authors_text":"Bernard Boigelot, Isabelle Mainz, Michel Rigo, Victor Marsault","submitted_at":"2017-02-13T10:51:45Z","abstract_excerpt":"Given an integer base $b>1$, a set of integers is represented in base $b$ by a language over $\\{0,1,...,b-1\\}$. The set is said to be $b$-recognisable if its representation is a regular language. It is known that eventually periodic sets are $b$-recognisable in every base $b$, and Cobham's theorem implies the converse: no other set is $b$-recognisable in every base $b$.\n  We are interested in deciding whether a $b$-recognisable set of integers (given as a finite automaton) is eventually periodic. Honkala showed that this problem decidable in 1986 and recent developments give efficient decision"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03715","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"}