{"paper":{"title":"Automaticity of one-relator semigroups with length less than or equal to three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Haibin Wu, Honglian Xie, Yuqun Chen","submitted_at":"2017-02-10T23:40:36Z","abstract_excerpt":"The main results of this paper is to give a complete characterization of the automaticity of one-relator semigroups with length less than or equal to three. Let $S=sgp\\langle A|u=v\\rangle$ be a semigroup generated by a set $A=\\{a_1,a_2,\\dots,a_n\\},\\ n\\in \\mathbb{N}$ with defining relation $u=v$, where $u,v\\in A^*$ and $A^*$ is the free monoid generated by $A$. Such a semigroup is called a one-relator semigroup. Suppose that $|v|\\leq|u|\\leq3$, where $|u|$ is the length of the word $u$. Suppose that $a,b\\in A,\\ a\\neq b$. Then we have the following: (1) $S$ is prefix-automatic if $u=v\\not\\in \\{ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03355","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"}