@inproceedings{849db49f5b1949dc88b12f42ae169d4b,

title = "Approaching the chasm at depth four",

abstract = "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})).",

keywords = "depth 4 circuits, determinant, lower bounds, partial derivatives, permanent",

author = "Ankit Gupta and Pritish Kamath and Neeraj Kayal and Ramprasad Saptharishi",

year = "2013",

doi = "10.1109/CCC.2013.16",

language = "אנגלית",

isbn = "9780769549972",

series = "Proceedings of the Annual IEEE Conference on Computational Complexity",

pages = "65--73",

booktitle = "Proceedings - 2013 IEEE Conference on Computational Complexity, CCC 2013",

note = "2013 IEEE Conference on Computational Complexity, CCC 2013 ; Conference date: 05-06-2013 Through 07-06-2013",

}