{"paper":{"title":"$\\mu$-Limit Sets of Cellular Automata from a Computational Complexity Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","nlin.CG"],"primary_cat":"cs.DM","authors_text":"Guillaume Theyssier (LAMA), Laurent Boyer (SAMM), Martin Delacourt (CMM), Mathieu Sablik (LATP), Victor Poupet (LIRMM)","submitted_at":"2013-09-26T06:30:59Z","abstract_excerpt":"This paper concerns $\\mu$-limit sets of cellular automata: sets of configurations made of words whose probability to appear does not vanish with time, starting from an initial $\\mu$-random configuration. More precisely, we investigate the computational complexity of these sets and of related decision problems. Main results: first, $\\mu$-limit sets can have a $\\Sigma\\_3^0$-hard language, second, they can contain only $\\alpha$-complex configurations, third, any non-trivial property concerning them is at least $\\Pi\\_3^0$-hard. We prove complexity upper bounds, study restrictions of these question"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6730","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"}