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**11 - 12**of**12**### Depth Reduction for Circuits with a Single Layer of Modular Counting Gates

"... We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC0◦MODm 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 probabi ..."

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We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC0◦MODm 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 probabilistic 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 ◦MODm 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 ◦MODm circuits. 1