### Approaching the Chasm at Depth FourApproaching the Chasm at Depth Four

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 Author Gupta, Ankit ♦ Kamath, Pritish ♦ Kayal, Neeraj ♦ Saptharishi, Ramprasad Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2014 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Determinant ♦ Arithmetic circuits ♦ Depth-4 circuits ♦ Lower bounds ♦ Partial derivatives ♦ Permanent Abstract Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp $(ω(√\textit{n}$ log $\textit{n}))$ lower bound for depth four homogeneous circuits computing the permanent with bottom layer of × gates having fanin bounded by √n translates to a superpolynomial lower bound for general arithmetic circuits computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin. We show here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by √n computing the permanent (or the determinant) must be of size $exp,(Ω(√\textit{n})).$ ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2014-12-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 61 Issue Number 6 Page Count 16 Starting Page 1 Ending Page 16

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Source: ACM Digital Library