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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