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A Spectral Lower Bound Technique for the Size of Decision Trees and Two-Level AND/OR Circuits
February 1990 (vol. 39 no. 2)
pp. 282-287

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.

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Index Terms:
spectral lower bound technique; decision trees; two-level AND/OR circuits; arbitrary Boolean function; power spectrum coefficients; n dimensional Fourier transform; Boolean functions; Fourier transforms; logic circuits; trees (mathematics).
Y. Brandman, A. Orlitsky, J. Hennessy, "A Spectral Lower Bound Technique for the Size of Decision Trees and Two-Level AND/OR Circuits," IEEE Transactions on Computers, vol. 39, no. 2, pp. 282-287, Feb. 1990, doi:10.1109/12.45216
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