{"paper":{"title":"A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Marco Voigt","submitted_at":"2017-04-07T09:10:37Z","abstract_excerpt":"Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time required to decide SF's satisfiability problem is formulated in terms of quantifier alternations: Given an SF sentence $\\exists \\vec{z} \\forall \\vec{x}_1 \\exists \\vec{y}_1 \\ldots \\forall \\vec{x}_n \\exists \\vec{y}_n . \\psi$ in which $\\psi$ is quantifier free, satisfiability can be decided in nondeterministic $n$-fold exponential time. In the present paper, we cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02145","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"}