{"paper":{"title":"Noncommutative Valiant's Classes: Structure and Complete Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Pushkar S Joglekar, S. Raja, V. Arvind","submitted_at":"2015-08-03T12:23:07Z","abstract_excerpt":"In this paper we explore the noncommutative analogues, $\\mathrm{VP}_{nc}$ and $\\mathrm{VNP}_{nc}$, of Valiant's algebraic complexity classes and show some striking connections to classical formal language theory. Our main results are the following: (1) We show that Dyck polynomials (defined from the Dyck languages of formal language theory) are complete for the class $\\mathrm{VP}_{nc}$ under $\\le_{abp}$ reductions. Likewise, it turns out that $\\mathrm{PAL}$ (Palindrome polynomials defined from palindromes) are complete for the class $\\mathrm{VSKEW}_{nc}$ (defined by polynomial-size skew circui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00395","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"}