{"paper":{"title":"Deterministic identity testing paradigms for bounded top-fanin depth-4 circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SC","math.AC"],"primary_cat":"cs.CC","authors_text":"Nitin Saxena, Pranjal Dutta, Prateek Dwivedi","submitted_at":"2023-04-22T05:36:12Z","abstract_excerpt":"Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth-$4$ reduction result by Agrawal and Vinay (FOCS 2008) has made PIT for depth-$4$ circuits an enticing pursuit. A restricted depth-4 circuit computing a $n$-variate degree-$d$ polynomial of the form $\\sum_{i = 1}^{k} \\prod_{j} g_{ij}$, where $\\deg g_{ij} \\leq \\delta$ is called $\\Sigma^{[k]}\\Pi\\Sigma\\Pi^{[\\delta]}$ circuit. On further restricting $g_{ij}$ to be sum of univariates we obtain $\\Sigma^{[k]}\\Pi\\Sigma\\wedge$ circuits. The largely open, special-cases of $\\Sigma^{[k]}\\Pi\\Sigma\\Pi^{[\\delta]}$ for c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.11325","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.11325/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}