{"paper":{"title":"Non-Redundancy of Low-Arity Symmetric Boolean CSPs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Symmetric Boolean CSPs of arity at most 5 have their non-redundancy growth rates classified as O(n), O(n^2), or O(n^3), with all arity-4 cases and most arity-5 cases resolved.","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Amatya Sharma, Santhoshini Velusamy","submitted_at":"2026-05-13T18:12:58Z","abstract_excerpt":"Non-redundancy, introduced by Bessiere, Carbonnel, and Katsirelos (AAAI 2020), is a structural parameter for Constraint Satisfaction Problems ($\\mathsf{CSPs}$) that governs kernelization, exact and approximate sparsification, and exact streaming complexity. It is the largest size of a $\\mathsf{CSP}$ instance admitting no smaller subinstance with the same satisfying assignments.\n  We study non-redundancy $\\mathsf{NRD}_n(R)$ for Boolean symmetric $\\mathsf{CSPs}$ defined by an $r$-ary relation $R$ whose value depends only on Hamming weight. An instance of $\\mathsf{CSP}(R)$ has $n$ variables and c"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result is a near-complete classification of the asymptotic growth of NRD_n(R) for symmetric Boolean predicates of arity at most 5. We resolve every predicate of arity at most 4 and all but two predicates of arity 5.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The computational experiments are assumed to have exhaustively enumerated and correctly classified all symmetric Boolean relations of arity at most 4 and all but two of arity 5; the algebraic criteria for t-balancedness are assumed to be tight for the unresolved cases.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symmetric Boolean CSPs of arity at most 5 have their non-redundancy growth rates classified as O(n), O(n^2), or O(n^3), with all arity-4 cases and most arity-5 cases resolved.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7e3a578c01d85ba6e1b54d44735c117b4c4889f4325a0b5be715000449af3e85"},"source":{"id":"2605.14007","kind":"arxiv","version":1},"verdict":{"id":"54f31192-e114-4be3-9373-9a4397d2f708","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:49:10.628545Z","strongest_claim":"Our main result is a near-complete classification of the asymptotic growth of NRD_n(R) for symmetric Boolean predicates of arity at most 5. We resolve every predicate of arity at most 4 and all but two predicates of arity 5.","one_line_summary":"Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The computational experiments are assumed to have exhaustively enumerated and correctly classified all symmetric Boolean relations of arity at most 4 and all but two of arity 5; the algebraic criteria for t-balancedness are assumed to be tight for the unresolved cases.","pith_extraction_headline":"Symmetric Boolean CSPs of arity at most 5 have their non-redundancy growth rates classified as O(n), O(n^2), or O(n^3), with all arity-4 cases and most arity-5 cases resolved."},"references":{"count":16,"sample":[{"doi":"","year":2012,"title":"Half-Approximating Maximum Dicut in the Streaming Setting","work_id":"b902cfef-5d2b-4f7a-971d-73300907962a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1109/focs.2019.00021.url:https://doi.org/10.1109/focs.2019.00021","year":2019,"title":"Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT","work_id":"2a6489cc-5f17-49ed-a87f-6b630c6ec80c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.4230/lipics.approx/random.2022","year":2022,"title":"Schloss Dagstuhl — Leibniz- Zentrum f ¨ur Informatik, July 2022, 38:1–38:23.DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022","work_id":"dcb4cb2b-3e1a-43da-b366-d3a9cd4e896a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3519935.3519983","year":2005,"title":"by Stefano Leonardi and Anupam Gupta","work_id":"9aec5d54-ecb0-4d1e-b646-03874b2aa8be","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"Near-Optimal Space Lower Bounds for Streaming CSPs","work_id":"b59e946f-e50f-4616-a6d4-bb1585259b7f","ref_index":5,"cited_arxiv_id":"2604.01400","is_internal_anchor":true}],"resolved_work":16,"snapshot_sha256":"5f350f5021c5ac003e7727f2ee5563dc0de8bf92e653a1e5f327bce32a3660ef","internal_anchors":3},"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"}