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Summary: Explicit Constructions of Depth-2 Majority Circuits for
Comparison and Addition
Noga Alon
IBM Research Division
Almaden Research Center
650 Harry Road
San Jose, CA 95120-6099
and Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
Jehoshua Bruck
IBM Research Division
Almaden Research Center
650 Harry Road
San Jose, CA 95120-6099
Abstract
All Boolean variables here range over the two element set {-1, 1}. Given n Boolean variables
x1, . . . , xn, a non-monotone MAJORITY gate (in the variables xi) is a Boolean function whose
value is the sign of
n
i=1 ixi, where each i is either 1 or -1. The COMPARISON function
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