DagSemProc.08381.4.pdf
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Depth Reduction for Circuits with a Single Layer of Modular Counting Gates
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Dagstuhl Seminar Proceedings, Volume 8381
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
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- Publication Date: 2008-12-17
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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
https://doi.org/10.4230/DagSemProc.08381.4
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.
Keywords
- Boolean Circuits
- Randomized Polynomials
- Fourier sums
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