{"paper":{"title":"The Complexity of Definability by Open First-Order Formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.CC","authors_text":"Carlos Areces, Daniel Penazzi, Miguel Campercholi, Pablo Ventura","submitted_at":"2019-04-09T13:10:24Z","abstract_excerpt":"In this article we formally define and investigate the computational complexity of the Definability Problem for open first-order formulas (i.e., quantifier free first-order formulas) with equality. Given a logic $\\mathbf{\\mathcal{L}}$, the $\\mathbf{\\mathcal{L}}$-Definability Problem for finite structures takes as input a finite structure $\\mathbf{A}$ and a target relation $T$ over the domain of $\\mathbf{A}$, and determines whether there is a formula of $\\mathbf{\\mathcal{L}}$ whose interpretation in $\\mathbf{A}$ coincides with $T$. We show that the complexity of this problem for open first-orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04637","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"}