{"paper":{"title":"Estimating the distance from testable affine-invariant properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hamed Hatami, Shachar Lovett","submitted_at":"2013-06-04T04:10:08Z","abstract_excerpt":"Let $\\cal{P}$ be an affine invariant property of functions $\\mathbb{F}_p^n \\to [R]$ for fixed $p$ and $R$. We show that if $\\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$ from $\\cal{P}$ with a constant number of queries. This was previously unknown even for simple properties such as cubic polynomials over $\\mathbb{F}_2$.\n  Our test is simple: take a restriction of $f$ to a constant dimensional affine subspace, and measure its distance from $\\cal{P}$. We show that by choosing the dimension large enough, this approximates with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0649","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"}