{"paper":{"title":"On the enumeration of signatures of XOR-CNF's","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Fr\\'ed\\'eric Olive, Nadia Creignou, Oscar Defrain, Simon Vilmin","submitted_at":"2024-02-28T18:22:03Z","abstract_excerpt":"Given a CNF formula $\\varphi$ with clauses $C_1, \\dots, C_m$ over a set of variables $V$, a truth assignment $\\mathbf{a} : V \\to \\{0, 1\\}$ generates a binary sequence $\\sigma_\\varphi(\\mathbf{a})=(C_1(\\mathbf{a}), \\ldots, C_m(\\mathbf{a}))$, called a signature of $\\varphi$, where $C_i(\\mathbf{a})=1$ if clause $C_i$ evaluates to 1 under assignment $\\mathbf{a}$, and $C_i(\\mathbf{a})=0$ otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, B\\'erczi et al. interestingly proved that generat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.18537","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.18537/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}