{"paper":{"title":"Constructive Analysis of S1S and B\\\"uchi Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Gert Smolka, Moritz Lichter","submitted_at":"2018-04-13T14:36:35Z","abstract_excerpt":"We study S1S and B\\\"uchi automata in the constructive type theory of the Coq proof assistant. For UP semantics (ultimately periodic sequences), we verify B\\\"uchi's translation of formulas to automata and thereby establish decidability of S1S constructively. For AS semantics (all sequences), we verify B\\\"uchi's translation assuming that sequences over finite semigroups have Ramseyan factorisations (RF). Assuming RF, UP semantics and AS semantics agree. RF is a consequence of Ramsey's theorem and implies the infinite pigeonhole principle, which is known to be unprovable constructively. We show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04967","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"}