{"paper":{"title":"Limitations of sum of products of Read-Once Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"B.V. Raghavendra Rao, C. Ramya","submitted_at":"2015-12-11T11:43:49Z","abstract_excerpt":"We study limitations of polynomials computed by depth two circuits built over read-once polynomials (ROPs) and depth three syntactically multi-linear formulas.\n  We prove an exponential lower bound for the size of the $\\Sigma\\Pi^{[N^{1/30}]}$ arithmetic circuits built over syntactically multi-linear $\\Sigma\\Pi\\Sigma^{[N^{8/15}]}$ arithmetic circuits computing a product of variable disjoint linear forms on $N$ variables. We extend the result to the case of $\\Sigma\\Pi^{[N^{1/30}]}$ arithmetic circuits built over ROPs of unbounded depth, where the number of variables with $+$ gates as a parent in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03607","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"}