{"paper":{"title":"Some Complete and Intermediate Polynomials in Algebraic Complexity Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Meena Mahajan, Nitin Saurabh","submitted_at":"2016-03-15T09:22:25Z","abstract_excerpt":"We provide a list of new natural $\\mathsf{VNP}$-intermediate polynomial families, based on basic (combinatorial) $\\mathsf{NP}$-complete problems that are complete under parsimonious reductions. Over finite fields, these families are in $\\mathsf{VNP}$, and under the plausible hypothesis $\\mathsf{Mod}_p\\mathsf{P} \\not\\subseteq \\mathsf{P/poly}$, are neither $\\mathsf{VNP}$-hard (even under oracle-circuit reductions) nor in $\\mathsf{VP}$. Prior to this, only the Cut Enumerator polynomial was known to be $\\mathsf{VNP}$-intermediate, as shown by B\\\"{u}rgisser in 2000.\n  We next show that over rationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04606","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"}