Tight bounds on communication complexity of symmetric XOR functions in one-way and SMP models

Authors:
Ming Lam Leung;Yang Li;Shengyu Zhang
Affiliations:
Department of Computer Science Engineering, The Institute of Theoretical Computer Science and Communications, The Chinese University of Hong Kong;Department of Computer Science Engineering, The Institute of Theoretical ComputerScience and Communications, The Chinese University of Hong Kong;Department of Computer Science Engineering, The Institute of Theoretical ComputerScience and Communications, The Chinese University of Hong Kong
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

Citing 7
Cited 0

Private vs. common random bits in communication complexity

Information Processing Letters
Communication complexity

Communication complexity
On the power of quantum fingerprinting

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)

STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The communication complexity of the Hamming distance problem

Information Processing Letters
Composition theorems in communication complexity

ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Communication complexities of symmetric XOR functions

Quantum Information & Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the communication complexity of symmetric XOR functions, namely functions f : {0, 1}n × {0, 1}n → {0, 1} that can be formulated as f(x, y) = D(|x ⊕ y|) for some predicate D : {0, 1, ..., n} → {0, 1}, where |x ⊕ y| is the Hamming weight of the bitwise XOR of x and y. We give a public-coin randomized protocol in the Simultaneous Message Passing (SMP) model, with the communication cost matching the known lower bound for the quantum and two-way model up to a logarithm factor. As a corollary, this closes a quadratic gap between the previous quantum lower bound and the randomized upper bound in the one-way model. This answers an open question raised in Shi and Zhang [SZ09], and disqualifies the problem from being a candidate to separate randomized and quantum one-way communication complexities.