Optimal Depth, Very Small Size Circuits for Symmetric Functions in AC0

@article{Hstad1994OptimalDV,
  title={Optimal Depth, Very Small Size Circuits for Symmetric Functions in AC0},
  author={Johan H{\aa}stad and Ingo Wegener and Norbert Wurm and Sang-Zin Yi},
  journal={Inf. Comput.},
  year={1994},
  volume={108},
  pages={200-211}
}
It is well-known which symmetric Boolean functions can be computed by constant depth, polynomial size, unbounded fan-in circuits, i.e. which are contained in the complexity class AC. This result is sharpened. Symmetric Boolean functions in AC can be computed by unbounded fan-in circuits with the following properties. If the optimal depth of ACcircuits is d, the depth is at most d + 2, the number of wires is almost linear, namely n log n, and the number of gates is subpolynomial (but… CONTINUE READING