{"paper":{"title":"Imperfect Gaps in Gap-ETH and PCPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mitali Bafna, Nikhil Vyas","submitted_at":"2019-07-18T17:48:19Z","abstract_excerpt":"We study the role of perfect completeness in probabilistically checkable proof systems (PCPs) and give a new way to transform a PCP with imperfect completeness to a PCP with perfect completeness when the initial gap is a constant. In particular, we show that $\\text{PCP}_{c,s}[r,q] \\subseteq \\text{PCP}_{1,1-\\Omega(1)}[r+O(1),q+O(r)]$, for $c-s=\\Omega(1)$. This implies that one can convert imperfect completeness to perfect in linear-sized PCPs for $NTIME[O(n)]$ with a $O(\\log n)$ additive loss in the query complexity $q$. We show our result by constructing a \"robust circuit\" using threshold gate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08185","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"}