COCOON 2012: Computing and Combinatorics pp 433-444

Formula Complexity of Ternary Majorities

• Kenya Ueno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)

Abstract

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.

Keywords

Boolean Function Majority Function Parity Function Decomposition Scheme Full Adder
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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