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- W232172244 abstract "We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of $(1/2-delta) cdot 2.57143^h$ for the two-sided-error randomized decision tree complexity of evaluating height $h$ formulae with error $delta in [0,1/2)$. This improves the lower bound of $(1-2delta)(7/3)^h$ given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of $(1-2delta) cdot 2.55^h$ given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero-error randomized decision tree algorithm that has complexity at most $(1.007) cdot 2.64944^h$. The previous best known algorithm achieved complexity $(1.004) cdot 2.65622^h$. The new lower bound follows from a better analysis of the base case of the recursion of Jayram et al. The new algorithm uses a novel interleaving of two recursive algorithms." @default.
- W232172244 created "2016-06-24" @default.
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- W232172244 date "2013-09-29" @default.
- W232172244 modified "2023-10-18" @default.
- W232172244 title "Improved bounds for the randomized decision tree complexity of recursive majority" @default.
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- W232172244 doi "https://doi.org/10.48550/arxiv.1309.7565" @default.
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