{"paper":{"title":"On Decidability Properties of One-Dimensional Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.LO"],"primary_cat":"cs.LO","authors_text":"LIP), Olivier Finkel (ELM","submitted_at":"2009-03-26T15:39:35Z","abstract_excerpt":"In a recent paper Sutner proved that the first-order theory of the phase-space $\\mathcal{S}_\\mathcal{A}=(Q^\\mathbb{Z}, \\longrightarrow)$ of a one-dimensional cellular automaton $\\mathcal{A}$ whose configurations are elements of $Q^\\mathbb{Z}$, for a finite set of states $Q$, and where $\\longrightarrow$ is the \"next configuration relation\", is decidable. He asked whether this result could be extended to a more expressive logic. We prove in this paper that this is actuallly the case. We first show that, for each one-dimensional cellular automaton $\\mathcal{A}$, the phase-space $\\mathcal{S}_\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4615","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"}