{"paper":{"title":"The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy","license":"","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.CC","authors_text":"Heinz Schmitz, Klaus W. Wagner","submitted_at":"1998-09-28T12:35:34Z","abstract_excerpt":"For some fixed alphabet A, a language L of A* is in the class L(1/2) of the Straubing-Therien hierarchy if and only if it can be expressed as a finite union of languages A*aA*bA*...A*cA*, where a,b,...,c are letters. The class L(1) is defined as the boolean closure of L(1/2). It is known that the classes L(1/2) and L(1) are decidable. We give a membership criterion for the single classes of the boolean hierarchy over L(1/2). From this criterion we can conclude that this boolean hierarchy is proper and that its classes are decidable.In finite model theory the latter implies the decidability of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/9809118","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"}