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Lower Bounds for Depth Three Arithmetic Circuits with Small Bottom Fanin Kayal, Neeraj Saha, Chandan arithmetic circuits depth three circuits lower bound bottom fanin Shpilka and Wigderson (CCC 99) had posed the problem of proving exponential lower bounds for (nonhomogeneous) depth three arithmetic circuits with bounded bottom fanin over a field F of characteristic zero. We resolve this problem by proving a N^(Omega(d/t)) lower bound for (nonhomogeneous) depth three arithmetic circuits with bottom fanin at most t computing an explicit N-variate polynomial of degree d over F. Meanwhile, Nisan and Wigderson (CC 97) had posed the problem of proving superpolynomial lower bounds for homogeneous depth five arithmetic circuits. Over fields of characteristic zero, we show a lower bound of N^(Omega(sqrt(d))) for homogeneous depth five circuits (resp. also for depth three circuits) with bottom fanin at most N^(u), for any fixed u < 1. This resolves the problem posed by Nisan and Wigderson only partially because of the added restriction on the bottom fanin (a general homogeneous depth five circuit has bottom fanin at most N). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Neeraj Kayal and Chandan Saha 2015 Is Part Of LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2015.158 urn:nbn:de:0030-drops-50617 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.158 eng https://creativecommons.org/licenses/by/3.0/legalcode