Related papers: A lower bound for bounded round quantum communicat…

We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive,…

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower…

For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…

We prove tight bounds of Theta(k log k) queries for non-adaptively testing whether a function f:{0,1}^n -> {0,1} is a k-parity or far from any k-parity. The lower bound combines a recent method of Blais, Brody and Matulef [BBM11] to get…

For integers $n$ and $k$, the density Hales-Jewett number $c_{n,k}$ is defined as the maximal size of a subset of $[k]^n$ that contains no combinatorial line. We show that for $k \ge 3$ the density Hales-Jewett number $c_{n,k}$ is equal to…

In a $k$-party communication problem, the $k$ players with inputs $x_1, x_2, \ldots, x_k$, respectively, want to evaluate a function $f(x_1, x_2, \ldots, x_k)$ using as little communication as possible. We consider the message-passing…

Building on the techniques behind the recent progress on the 3-term arithmetic progression problem [KM'23], Kelley, Lovett, and Meka [KLM'24] constructed the first explicit 3-player function $f:[N]^3 \rightarrow \{0,1\}$ that demonstrates a…

Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on…

Buhrman, Cleve and Wigderson (STOC'98) showed that for every Boolean function f : {-1,1}^n to {-1,1} and G in {AND_2, XOR_2}, the bounded-error quantum communication complexity of the composed function f o G equals O(Q(f) log n), where Q(f)…

We prove an \Omega(n/k+k) communication lower bound on (k-1)-round distributional complexity of the k-step pointer chasing problem under uniform input distribution, improving the \Omega(n/k - k log n) lower bound due to Yehudayoff…

We propose a linear algebraic method, rooted in the spectral properties of graphs, that can be used to prove lower bounds in communication complexity. Our proof technique effectively marries spectral bounds with information-theoretic…

We study the CHAIN communication problem introduced by Cormode et al. [ICALP 2019]. It is a generalization of the well-studied INDEX problem. For $k\geq 1$, in CHAIN$_{n,k}$, there are $k$ instances of INDEX, all with the same answer. They…

We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that…

We derive lower bounds for tradeoffs between the communication C and space S for communicating circuits. The first such bound applies to quantum circuits. If for any function f with image Z the multicolor discrepancy of the communication…

We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…

We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…

This paper studies the one-way communication complexity of the subgroup membership problem, a classical problem closely related to basic questions in quantum computing. Here Alice receives, as input, a subgroup $H$ of a finite group $G$;…

Estimating the second frequency moment $F_2$ of a data stream up to a $(1 \pm \varepsilon)$ factor is a central problem in the streaming literature. For errors $\varepsilon > \Omega(1/\sqrt{n})$, the tight bound…

In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…

We study the round and communication complexities of various cryptographic protocols. We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from…