{"paper":{"title":"Generating Matrix Identities and Proof Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Fu Li, Iddo Tzameret","submitted_at":"2013-12-21T11:32:41Z","abstract_excerpt":"Motivated by the fundamental lower bounds questions in proof complexity, we initiate the study of matrix identities as hard instances for strong proof systems. A matrix identity of $d \\times d$ matrices over a field $\\mathbb{F}$, is a non-commutative polynomial $f(x_1,\\ldots,x_n)$ over $\\mathbb{F}$ such that $f$ vanishes on every $d \\times d$ matrix assignment to its variables.\n  We focus on arithmetic proofs, which are proofs of polynomial identities operating with arithmetic circuits and whose axioms are the polynomial-ring axioms (these proofs serve as an algebraic analogue of the Extended "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6242","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"}