On read-once threshold formulae and their randomized decision tree complexity
Theoretical Computer Science - Special issue on structure in complexity theory
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Improved bounds for the randomized decision tree complexity of recursive majority
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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We prove that the randomized decision tree complexity of the recursive majority-of-three is Ω(2.55d), where d is the depth of the recursion. The proof is by a bottom up induction, which is same in spirit as the one in the proof of Saks and Wigderson in their 1986 paper on the complexity of evaluating game trees. Previous work includes an $\Omega\bigl((7/3)^d\bigr)$ lower bound, published in 2003 by Jayram, Kumar, and Sivakumar. Their proof used a top down induction and tools from information theory. In 2011, Magniez, Nayak, Santha, and Xiao, improved the lower bound to $\Omega\bigl((5/2)^d\bigr)$ and the upper bound to O(2.64946d).