{"paper":{"title":"Towards an algebraic natural proofs barrier via polynomial identity testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"Joshua A. Grochow, Michael Saks, Mrinal Kumar, Shubhangi Saraf","submitted_at":"2017-01-06T18:27:48Z","abstract_excerpt":"We observe that a certain kind of algebraic proof - which covers essentially all known algebraic circuit lower bounds to date - cannot be used to prove lower bounds against VP if and only if what we call succinct hitting sets exist for VP. This is analogous to the Razborov-Rudich natural proofs barrier in Boolean circuit complexity, in that we rule out a large class of lower bound techniques under a derandomization assumption. We also discuss connections between this algebraic natural proofs barrier, geometric complexity theory, and (algebraic) proof complexity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01717","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"}