{"paper":{"title":"Polynomially Low Error PCPs with polyloglog n Queries via Modular Composition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Guy Kindler, Irit Dinur, Prahladh Harsha","submitted_at":"2015-05-23T18:56:33Z","abstract_excerpt":"We show that every language in NP has a PCP verifier that tosses $O(\\log n)$ random coins, has perfect completeness, and a soundness error of at most $1/\\text{poly}(n)$, while making at most $O(\\text{poly}\\log\\log n)$ queries into a proof over an alphabet of size at most $n^{1/\\text{poly}\\log\\log n}$. Previous constructions that obtain $1/\\text{poly}(n)$ soundness error used either $\\text{poly}\\log n $ queries or an exponential sized alphabet, i.e. of size $2^{n^c}$ for some $c>0$. Our result is an exponential improvement in both parameters simultaneously.\n  Our result can be phrased as a poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06362","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"}