Formula Complexity of Ternary Majorities
It is known that any self-dual Boolean function can be decomposed into compositions of 3-bit majority functions. In this paper, we define a notion of a ternary majority formula, which is a ternary tree composed of nodes labeled by 3-bit majority functions and leaves labeled by literals. We study their complexity in terms of formula size. In particular, we prove upper and lower bounds for ternary majority formula size of several Boolean functions. To devise a general method to prove the ternary majority formula size lower bounds, we give an upper bound for the largest separation between ternary majority formula size and DeMorgan formula size.
KeywordsBoolean Function Majority Function Parity Function Decomposition Scheme Full Adder
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