{"paper":{"title":"Near Optimal Alphabet-Soundness Tradeoff PCPs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Dor Minzer, Kai Zhe Zheng","submitted_at":"2024-04-11T02:51:35Z","abstract_excerpt":"We show that for all $\\varepsilon>0$, for sufficiently large $q\\in\\mathbb{N}$ power of $2$, for all $\\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least $1-\\delta$, or value at most $1/q^{1-\\varepsilon}$. This establishes a nearly optimal alphabet-to-soundness tradeoff for $2$-query PCPs with alphabet size $q$, improving upon a result of [Chan, Journal of the ACM 2016]. Our result has the following implications:\n  1) Near optimal hardness for Quadratic Programming: it is NP-hard to approximate the value of a giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07441","kind":"arxiv","version":4},"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"}