{"paper":{"title":"Quadratization of Symmetric Pseudo-Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CV","math.CO"],"primary_cat":"math.OC","authors_text":"Aritanan Gruber, Endre Boros, Martin Anthony, Yves Crama","submitted_at":"2014-04-25T20:00:22Z","abstract_excerpt":"A pseudo-Boolean function is a real-valued function $f(x)=f(x_1,x_2,\\ldots,x_n)$ of $n$ binary variables; that is, a mapping from $\\{0,1\\}^n$ to $\\mathbb{R}$. For a pseudo-Boolean function $f(x)$ on $\\{0,1\\}^n$, we say that $g(x,y)$ is a quadratization of $f$ if $g(x,y)$ is a quadratic polynomial depending on $x$ and on $m$ auxiliary binary variables $y_1,y_2,\\ldots,y_m$ such that $f(x)= \\min \\{g(x,y) : y \\in \\{0,1\\}^m \\}$ for all $x \\in \\{0,1\\}^n$. By means of quadratizations, minimization of $f$ is reduced to minimization (over its extended set of variables) of the quadratic function $g(x,y)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6535","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"}