{"paper":{"title":"A Language Hierarchy and Kitchens-Type Theorem for Self-Similar Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrew Penland, Zoran \\v{S}uni\\'c","submitted_at":"2017-10-08T21:09:17Z","abstract_excerpt":"We generalize the notion of self-similar groups of infinite tree automorphisms to allow for groups which are defined on a tree but do not act faithfully on it. The elements of such a group correspond to labeled trees which may be recognized by a tree automaton (e.g. Rabin, B\\\"{u}chi, etc.), or considered as elements of a tree shift (e.g. of finite type, sofic) as in symbolic dynamics. We give examples to show that the various classes of self-similar groups defined in this way do not coincide. As the main result, extending the classical result of Kitchens on one-dimensional group shifts, we pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02886","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"}