{"paper":{"title":"On the Parity Problem in One-Dimensional Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","nlin.CG"],"primary_cat":"cs.FL","authors_text":"Brazil), Canada), Heater Betel (University of Ottawa, Paola Flocchini (University of Ottawa, Pedro P. B. de Oliveira (Universidade Presbiteriana Mackenzie","submitted_at":"2012-08-14T01:54:58Z","abstract_excerpt":"We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices.\n  We are interested in determining the minimal neighbourhood that allows the problem to be solvable for any initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2758","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"}