Approaching the chasm at depth four

Ankit Gupta, Pritish Kamath, Neeraj Kayal, Ramprasad Saptharishi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Agrawal-Vinay [AV08] and Koiran [Koi12] have recently shown that an exp(omega(sqrt{n}log2 n)) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of x gates having fanin bounded by sqrt{n} translates to super-polynomial 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 sqrt{n} computing the permanent (or the determinant) must be of size exp(Omega(sqrt{n})).

Original languageEnglish
Title of host publicationProceedings - 2013 IEEE Conference on Computational Complexity, CCC 2013
Number of pages9
StatePublished - 2013
Externally publishedYes
Event2013 IEEE Conference on Computational Complexity, CCC 2013 - Palo Alto, CA, United States
Duration: 5 Jun 20137 Jun 2013

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159


Conference2013 IEEE Conference on Computational Complexity, CCC 2013
Country/TerritoryUnited States
CityPalo Alto, CA


  • depth 4 circuits
  • determinant
  • lower bounds
  • partial derivatives
  • permanent


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