{"paper":{"title":"Profinite automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.NT"],"primary_cat":"math.DS","authors_text":"Eric Rowland, Reem Yassawi","submitted_at":"2014-03-29T18:36:55Z","abstract_excerpt":"Many sequences of $p$-adic integers project modulo $p^\\alpha$ to $p$-automatic sequences for every $\\alpha \\geq 0$. Examples include algebraic sequences of integers, which satisfy this property for every prime $p$, and some cocycle sequences, which we show satisfy this property for a fixed $p$. For such a sequence, we construct a profinite automaton that projects modulo $p^\\alpha$ to the automaton generating the projected sequence. In general, the profinite automaton has infinitely many states. Additionally, we consider the closure of the orbit, under the shift map, of the $p$-adic integer seq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7659","kind":"arxiv","version":4},"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"}