{"paper":{"title":"Quasi-Linear Size PCPs with Small Soundness from HDX","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dor Minzer, Mitali Bafna, Nikhil Vyas","submitted_at":"2024-07-17T17:39:42Z","abstract_excerpt":"We construct 2-query, quasi-linear size probabilistically checkable proofs (PCPs) with arbitrarily small constant soundness, improving upon Dinur's 2-query quasi-linear size PCPs with soundness $1-\\Omega(1)$. As an immediate corollary, we get that under the exponential time hypothesis, for all $\\epsilon>0$ no approximation algorithm for $3$-SAT can obtain an approximation ratio of $7/8+\\epsilon$ in time $2^{n/\\log^C n}$, where $C$ is a constant depending on $\\epsilon$. Our result builds on a recent line of independent works by Bafna, Lifshitz and Minzer, and Dikstein, Dinur and Lubotzky, that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12762","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.12762/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}