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URN: urn:nbn:de:0030-drops-17824
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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:DagSemProc.08381.4,
  author =	{Hansen, Kristoffer Arnsfelt},
  title =	{{Depth Reduction for Circuits with a Single Layer of Modular Counting Gates}},
  booktitle =	{Computational Complexity of Discrete Problems},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8381},
  editor =	{Peter Bro Miltersen and R\"{u}diger Reischuk and Georg Schnitger and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2008/1782},
  URN =		{urn:nbn:de:0030-drops-17824},
  doi =		{10.4230/DagSemProc.08381.4},
  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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