An Improved Lower Bound for the Randomized Decision Tree Complexity of Recursive Majority,
نویسنده
چکیده
We prove that the randomized decision tree complexity of the recursive majority-of-three is Ω(2.55), 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 Ω (
منابع مشابه
Improved bounds for the randomized decision tree complexity
We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of (1/2 − δ) · 2.57143 for the two-sided-error randomized decision tree complexity of evaluating height h formulae with error δ ∈ [0, 1/2). This improves the lower bound of (1 − 2δ)(7/3) given by Jayram, Kumar, and Sivakumar (STOC’03), and the one of (1 − 2δ) · 2.55 given by Leonardo...
متن کاملSeparating Decision Tree Complexity from Subcube Partition Complexity
The subcube partition model of computation is at least as powerful as decision trees but no separation between these models was known. We show that there exists a function whose deterministic subcube partition complexity is asymptotically smaller than its randomized decision tree complexity, resolving an open problem of Friedgut, Kahn, and Wigderson (2002). Our lower bound is based on the infor...
متن کاملImproved 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 δ-two-sided-error randomized decision tree complexity of (1 − 2δ)(5/2), improving the lower bound of (1 − 2δ)(7/3) given by Jayram et al. (STOC ’03). We also state a conjecture which would further improve the lower bound to (1− 2δ)2.54355. ...
متن کاملAn inequality for the Fourier spectrum of parity decision trees
We give a new bound on the sum of the linear Fourier coefficients of a Boolean function in terms of its parity decision tree complexity. This result generalizes an inequality of O’Donnell and Servedio for regular decision trees [OS08]. We use this bound to obtain the first non-trivial lower bound on the parity decision tree complexity of the recursive majority function.
متن کاملA Composition Theorem for Conical Juntas
We describe a general method of proving degree lower bounds for conical juntas (nonnegative combinations of conjunctions) that compute recursively defined boolean functions. Such lower bounds are known to carry over to communication complexity. We give two applications: • AND-OR trees. We show a near-optimal Ω̃(n0.753...) randomised communication lower bound for the recursive NAND function (a.k....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012