Depth Reduction for Circuits of Unbounded Fan-in

E. Allender, U. Hertrampf
1994 Information and Computation  
We prove that constant depth circuits of size n log O(1) n over the basis AND, OR, PARITY are no more powerful than circuits of this size with depth four. Similar techniques are used to obtain several other depth reduction theorems; in particular, we show every set in AC 0 can be recognized by a family of depththree threshold circuits of size n log O(1) n . The size bound n log O(1) n is optimal when considering depth reduction over AND, OR, and PARITY. Most of our results hold both for the uniform and the nonuniform case.
doi:10.1006/inco.1994.1057 fatcat:ofxkaojqq5dzberra5iaegzt4q