Title :
A spectral lower bound technique for the size of decision trees and two-level AND/OR circuits
Author :
Brandman, Yigal ; Orlitsky, Alon ; Hennessy, John
Author_Institution :
Dept. of Electr. Eng., Stanford Univ., CA, USA
fDate :
2/1/1990 12:00:00 AM
Abstract :
A universal lower-bound technique for the size and other implementation characteristics of an arbitrary Boolean function as a decision tree and as a two-level AND/OR circuit is derived. The technique is based on the power spectrum coefficients of the n dimensional Fourier transform of the function. The bounds vary from constant to exponential and are tight in many cases. Several examples are presented
Keywords :
Boolean functions; Fourier transforms; logic circuits; trees (mathematics); arbitrary Boolean function; decision trees; n dimensional Fourier transform; power spectrum coefficients; spectral lower bound technique; two-level AND/OR circuits; Binary trees; Boolean functions; Circuit synthesis; Complexity theory; Decision trees; Fourier transforms; Input variables; Labeling; Logic circuits; Programmable logic arrays;
Journal_Title :
Computers, IEEE Transactions on
