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

Hansen, Kristoffer Arnsfelt

doi:10.4230/DagSemProc.08381.4

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

Author Kristoffer Arnsfelt Hansen

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 8381
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2008-12-17

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DagSemProc.08381.4.pdf

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DOI: 10.4230/DagSemProc.08381.4
URN: urn:nbn:de:0030-drops-17824

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Keywords

Boolean Circuits
Randomized Polynomials
Fourier sums

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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.

Cite As Get BibTex

Kristoffer Arnsfelt Hansen. Depth Reduction for Circuits with a Single Layer of Modular Counting Gates. In Computational Complexity of Discrete Problems. Dagstuhl Seminar Proceedings, Volume 8381, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008) https://doi.org/10.4230/DagSemProc.08381.4

Author Details

Kristoffer Arnsfelt Hansen

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