{"paper":{"title":"Local reductions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Emanuele Viola, Eric Miles, Hamid Jahanjou","submitted_at":"2013-11-13T15:28:37Z","abstract_excerpt":"We reduce non-deterministic time $T \\ge 2^n$ to a 3SAT instance $\\phi$ of quasilinear size $|\\phi| = T \\cdot \\log^{O(1)} T$ such that there is an explicit circuit $C$ that on input an index $i$ of $\\log |\\phi|$ bits outputs the $i$th clause, and each output bit of $C$ depends on $O(1)$ input bits. The previous best result was $C$ in NC$^1$. Even in the simpler setting of polynomial size $|\\phi| = \\poly(T)$ the previous best result was $C$ in AC$^0$.\n  More generally, for any time $T \\ge n$ and parameter $r \\leq n$ we obtain $\\log_2 |\\phi| = \\max(\\log T, n/r) + O(\\log n) + O(\\log\\log T)$ and ea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3171","kind":"arxiv","version":3},"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"}