{"paper":{"title":"Efficient deterministic approximate counting for low-degree polynomial threshold functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"cs.CC","authors_text":"Anindya De, Rocco Servedio","submitted_at":"2013-11-28T00:00:59Z","abstract_excerpt":"We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\\dots,x_n)$ over $R^n$ and a parameter $\\epsilon> 0$, our algorithm approximates $\\Pr_{x \\sim \\{-1,1\\}^n}[p(x) \\geq 0]$ to within an additive $\\pm \\epsilon$ in time $O_{d,\\epsilon}(1)\\cdot \\mathop{poly}(n^d)$. (Any sort of efficient multiplicative approximation is impossible even for randomized algorithms assuming $NP\\not=RP$.) Note that the running time of our algorithm (as a function of $n^d$, the number of coeffic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7178","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"}