{"paper":{"title":"Cost and dimension of words of zero topological entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Anna E. Frid, Julien Cassaigne, Luca Q. Zamboni, Svetlana Puzynina","submitted_at":"2016-07-16T11:42:29Z","abstract_excerpt":"Let $A^*$ denote the free monoid generated by a finite nonempty set $A.$ In this paper we introduce a new measure of complexity of languages $L\\subseteq A^*$ defined in terms of the semigroup structure on $A^*.$ For each $L\\subseteq A^*,$ we define its {\\it cost} $c(L)$ as the infimum of all real numbers $\\alpha$ for which there exist a language $S\\subseteq A^*$ with $p_S(n)=O(n^\\alpha)$ and a positive integer $k$ with $L\\subseteq S^k.$ We also define the {\\it cost dimension} $d_c(L)$ as the infimum of the set of all positive integers $k$ such that $L\\subseteq S^k$ for some language $S$ with $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04728","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"}