{"paper":{"title":"Fast Exact Algorithms Using Hadamard Product of Polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Abhranil Chatterjee, Partha Mukhopadhyay, Rajit Datta, V.Arvind","submitted_at":"2018-07-12T09:34:29Z","abstract_excerpt":"Let $C$ be an arithmetic circuit of $poly(n)$ size given as input that computes a polynomial $f\\in\\mathbb{F}[X]$, where $X=\\{x_1,x_2,\\ldots,x_n\\}$ and $\\mathbb{F}$ is any field where the field arithmetic can be performed efficiently. We obtain new algorithms for the following two problems first studied by Koutis and Williams \\cite{Kou08, Wi09, KW16}. k-MLC: Compute the sum of the coefficients of all degree-$k$ multilinear monomials in the polynomial $f$. k-MMD: Test if there is a nonzero degree-$k$ multilinear monomial in the polynomial $f$.\n  Our algorithms are based on the fact that the Hada"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04496","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/1807.04496/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"}