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URN: urn:nbn:de:0030-drops-17824
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1782/
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Hansen, Kristoffer Arnsfelt

Depth Reduction for Circuits with a Single Layer of Modular Counting Gates

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Abstract

We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e ${AC}^0 circ {MOD}_m$ circuits. We show that the following holds for several types of gates $G$: by adding a gate of type $G$ at the output, it is possible to obtain an equivalent randomized depth 2 circuit of quasipolynomial size consisting of a gate of type $G$ at the output and a layer of modular counting gates, i.e $G circ {MOD}_m$ circuits. The types of gates $G$ we consider are modular counting gates and threshold-style gates. For all of these, strong lower bounds are known for (deterministic) $G circ {MOD}_m$ circuits.

BibTeX - Entry

@InProceedings{hansen:DSP:2008:1782,
  author =	{Kristoffer Arnsfelt Hansen},
  title =	{Depth Reduction for Circuits with a Single Layer of Modular Counting Gates},
  booktitle =	{Computational Complexity of Discrete Problems },
  year =	{2008},
  editor =	{Peter Bro Miltersen and R{\"u}diger Reischuk and Georg Schnitger and Dieter van Melkebeek},
  number =	{08381},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1782},
  annote =	{Keywords: Boolean Circuits, Randomized Polynomials, Fourier sums}
}

Keywords: Boolean Circuits, Randomized Polynomials, Fourier sums
Seminar: 08381 - Computational Complexity of Discrete Problems
Issue Date: 2008
Date of publication: 17.12.2008

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