{"paper":{"title":"Depth-4 Lower Bounds, Determinantal Complexity : A Unified Approach","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Partha Mukhopadhyay, Suryajith Chillara","submitted_at":"2013-08-07T17:21:16Z","abstract_excerpt":"Tavenas has recently proved that any n^{O(1)}-variate and degree n polynomial in VP can be computed by a depth-4 circuit of size 2^{O(\\sqrt{n}\\log n)}. So to prove VP not equal to VNP, it is sufficient to show that an explicit polynomial in VNP of degree n requires 2^{\\omega(\\sqrt{n}\\log n)} size depth-4 circuits. Soon after Tavenas's result, for two different explicit polynomials, depth-4 circuit size lower bounds of 2^{\\Omega(\\sqrt{n}\\log n)} have been proved Kayal et al. and Fournier et al. In particular, using combinatorial design Kayal et al.\\ construct an explicit polynomial in VNP that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1640","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"}