{"paper":{"title":"Amenability of groups is characterized by Myhill's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"cs.FL","authors_text":"Dawid Kielak, Laurent Bartholdi","submitted_at":"2016-05-30T08:14:59Z","abstract_excerpt":"We prove a converse to Myhill's \"Garden-of-Eden\" theorem and obtain in this manner a characterization of amenability in terms of cellular automata: \"A group $G$ is amenable if and only if every cellular automaton with carrier $G$ that has gardens of Eden also has mutually erasable patterns.\"\n  This answers a question by Schupp, and solves a conjecture by Ceccherini-Silberstein, Mach\\`i and Scarabotti.\n  An appendix by Dawid Kielak proves that group rings without zero divisors are Ore domains precisely when the group is amenable, answering a conjecture attributed to Guba."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09133","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"}