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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.
Date of Publication: April 1971