Improved bounds for the randomized decision tree complexity of recursive majority

We consider the randomized decision tree complexity of the recursive 3-majority function. For evaluating a height h formulae, we prove a lower bound for the -two-sided-error randomized decision tree complexity of (1 - 2)(5/2)h , improving the lower bound of (1 - 2)(7/3)h given by Jayram et al. (STOC '03). We also state a conjecture which would further improve the lower bound to (1 - 2)2.54355h . Second, we improve the upper bound by giving a new zero-error randomized decision tree algorithm

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Frédéric Magniez, Ashwin Nayak, Miklos Santha, David Xiao
• Keywords: Decision Tree, ECCC 2010, Hardware, Lower Bound, Randomized Decision Tree