{"paper":{"title":"Decidable Characterization of FO2(<,+1) and locality of DA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Luc Segoufin, Thomas Place","submitted_at":"2016-06-10T07:45:53Z","abstract_excerpt":"Several years ago Th\\'erien and Wilke exhibited a decidable characterization of the languages of words that are definable in FO2(<,+1). Their proof relies on three separate ingredients. The first one is the characterization of the languages that are definable in FO2(<) as those whose syntactic semigroup belongs to the variety DA. Then, this result is combined with a wreath product argument showing that being definable in FO2(<,+1) corresponds to having a syntactic semigroup in DA*D. Finally, proving that membership of a semigroup in DA*D is decidable requires a third ingredient: the \"locality\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03217","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"}