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DOI: 10.4230/LIPIcs.STACS.2015.527
URN: urn:nbn:de:0030-drops-49395
URL: http://drops.dagstuhl.de/opus/volltexte/2015/4939/
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Kayal, Neeraj ; Saha, Chandan

Multi-k-ic Depth Three Circuit Lower Bound

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Abstract

In a multi-k-ic depth three circuit every variable appears in at most k of the linear polynomials in every product gate of the circuit. This model is a natural generalization of multilinear depth three circuits that allows the formal degree of the circuit to exceed the number of underlying variables (as the formal degree of a multi-k-ic depth three circuit can be kn where n is the number of variables). The problem of proving lower bounds for depth three circuits with high formal degree has gained in importance following a work by Gupta, Kamath, Kayal and Saptharishi [7] on depth reduction to high formal degree depth three circuits. In this work, we show an exponential lower bound for multi-k-ic depth three circuits for any arbitrary constant k.

BibTeX - Entry

@InProceedings{kayal_et_al:LIPIcs:2015:4939,
  author =	{Neeraj Kayal and Chandan Saha},
  title =	{{Multi-k-ic Depth Three Circuit Lower Bound}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{527--539},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4939},
  URN =		{urn:nbn:de:0030-drops-49395},
  doi =		{10.4230/LIPIcs.STACS.2015.527},
  annote =	{Keywords: arithmetic circuits, multilinear circuits, depth three circuits, lower bound, individual degree}
}

Keywords: arithmetic circuits, multilinear circuits, depth three circuits, lower bound, individual degree
Seminar: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 25.02.2015


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