{"paper":{"title":"Randomized Polynomial Time Identity Testing for Noncommutative Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Partha Mukhopadhyay, S. Raja, V. Arvind","submitted_at":"2016-06-02T09:33:02Z","abstract_excerpt":"In this paper we show that the black-box polynomial identity testing for noncommutative polynomials $f\\in\\mathbb{F}\\langle z_1,z_2,\\cdots,z_n \\rangle$ of degree $D$ and sparsity $t$, can be done in randomized $\\poly(n,\\log t,\\log D)$ time. As a consequence, if the black-box contains a circuit $C$ of size $s$ computing $f\\in\\mathbb{F}\\langle z_1,z_2,\\cdots,z_n \\rangle$ which has at most $t$ non-zero monomials, then the identity testing can be done by a randomized algorithm with running time polynomial in $s$ and $n$ and $\\log t$. This makes significant progress on a question that has been open "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00596","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"}