{"paper":{"title":"Efficient Identity Testing and Polynomial Factorization over Non-associative Free Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Partha Mukhopadhyay, Rajit Datta, S. Raja, V. Arvind","submitted_at":"2017-04-29T07:04:07Z","abstract_excerpt":"In this paper we study arithmetic computations in the nonassociative, and noncommutative free polynomial ring $\\mathbb{F}\\{x_1,x_2,\\ldots,x_n\\}$. Prior to this work, nonassociative arithmetic computation was considered by Hrubes, Wigderson, and Yehudayoff [HWY10], and they showed lower bounds and proved completeness results. We consider Polynomial Identity Testing (PIT) and polynomial factorization over $\\mathbb{F}\\{x_1,x_2,\\ldots,x_n\\}$ and show the following results. (1) Given an arithmetic circuit $C$ of size $s$ computing a polynomial $f\\in \\mathbb{F} \\{x_1,x_2,\\ldots,x_n\\}$ of degree $d$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00140","kind":"arxiv","version":2},"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"}