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arXiv · 1101.4555

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

Ming Lam Leung·Yang Li·Shengyu Zhang
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Abstract

We study the communication complexity of symmetric XOR functions, namely functions $f: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ that can be formulated as $f(x,y)=D(|x\oplus y|)$ for some predicate $D: \{0,1,...,n\} \rightarrow \{0,1\}$, where $|x\oplus y|$ 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 \emph{quantum} and \emph{two-way} model up to a logarithm factor. As a corollary, this closes a quadratic gap between quantum lower bound and randomized upper bound for the one-way model, answering an open question raised in Shi and Zhang \cite{SZ09}.

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Ming Lam Leung, Yang Li, Shengyu Zhang. 2011-01-24. Tight bounds on the randomized communication complexity of symmetric XOR functions in one-way and SMP models. https://doi.org/10.1007/978-3-642-20877-5_39

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