{"paper":{"title":"Deterministic Approximate Counting for Juntas of Degree-$2$ Polynomial Threshold Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.CC","authors_text":"Anindya De, Ilias Diakonikolas, Rocco A. Servedio","submitted_at":"2013-11-27T20:33:33Z","abstract_excerpt":"Let $g: \\{-1,1\\}^k \\to \\{-1,1\\}$ be any Boolean function and $q_1,\\dots,q_k$ be any degree-2 polynomials over $\\{-1,1\\}^n.$ We give a \\emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\\dots,q_k$ and an accuracy parameter $\\eps>0$, approximates \\[\\Pr_{x \\sim \\{-1,1\\}^n}[g(\\sign(q_1(x)),\\dots,\\sign(q_k(x)))=1]\\] to within an additive $\\pm \\eps$. For any constant $\\eps > 0$ and $k \\geq 1$ the running time of our algorithm is a fixed polynomial in $n$. This is the first fixed polynomial-time algorithm that can deterministically approximately count satisfying assi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7115","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"}