{"paper":{"title":"On teaching sets of k-threshold functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elena Zamaraeva","submitted_at":"2015-02-15T18:01:08Z","abstract_excerpt":"Let $f$ be a $\\{0,1\\}$-valued function over an integer $d$-dimensional cube $\\{0,1,\\dots,n-1\\}^d$, for $n \\geq 2$ and $d \\geq 1$. The function $f$ is called threshold if there exists a hyperplane which separates $0$-valued points from $1$-valued points. Let $C$ be a class of functions and $f \\in C$. A point $x$ is essential for the function $f$ with respect to $C$ if there exists a function $g \\in C$ such that $x$ is a unique point on which $f$ differs from $g$. A set of points $X$ is called teaching for the function $f$ with respect to $C$ if no function in $C \\setminus \\{f\\}$ agrees with $f$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04340","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":""},"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"}