{"paper":{"title":"On fixed-polynomial size circuit lower bounds for uniform polynomials in the sense of Valiant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Herv\\'e Fournier, R\\'emi de Verclos, Sylvain Perifel","submitted_at":"2013-04-22T10:42:03Z","abstract_excerpt":"Assuming the Generalised Riemann Hypothesis (GRH), we show that for all k, there exist polynomials with coefficients in $\\MA$ having no arithmetic circuits of size O(n^k) over the complex field (allowing any complex constant). We also build a family of polynomials that can be evaluated in AM having no arithmetic circuits of size O(n^k). Then we investigate the link between fixed-polynomial size circuit bounds in the Boolean and arithmetic settings. In characteristic zero, it is proved that $\\NP \\not\\subset \\size(n^k)$, or $\\MA \\subset \\size(n^k)$, or NP=MA imply lower bounds on the circuit siz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5910","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"}