{"paper":{"title":"Fooling intersections of low-weight halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Li-Yang Tan, Rocco A. Servedio","submitted_at":"2017-04-17T03:18:11Z","abstract_excerpt":"A weight-$t$ halfspace is a Boolean function $f(x)=$sign$(w_1 x_1 + \\cdots + w_n x_n - \\theta)$ where each $w_i$ is an integer in $\\{-t,\\dots,t\\}.$ We give an explicit pseudorandom generator that $\\delta$-fools any intersection of $k$ weight-$t$ halfspaces with seed length poly$(\\log n, \\log k,t,1/\\delta)$. In particular, our result gives an explicit PRG that fools any intersection of any quasipoly$(n)$ number of halfspaces of any poly$\\log(n)$ weight to any $1/$poly$\\log(n)$ accuracy using seed length poly$\\log(n).$ Prior to this work no explicit PRG with non-trivial seed length was known eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04855","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"}