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On the Delay Required to Realize Boolean Functions
April 1971 (vol. 20 no. 4)
pp. 459-461
Using as logic modules two-input one-output arbitrary logic gates, this note considers the problem of the longest chain (number of levels) in a tree-type interconnection realizing a Boolean function of n variables. Specifically, we are interested in the minimum number of levels L(n) by which we can constructively realize all Boolean functions of n variables. It was previously shown that L(n)=n for n=3, 4 and it was so conjectured for n= 5; in this note we are able to show that this holds for n=5, 6, 7, 8.
Index Terms:
Computational complexity, conjuctive decomposition, realization delay, switching functions.
F.P. Preparata, D.E. Muller, "On the Delay Required to Realize Boolean Functions," IEEE Transactions on Computers, vol. 20, no. 4, pp. 459-461, April 1971, doi:10.1109/T-C.1971.223266
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