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We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on…
We develop a novel and powerful technique for communication lower bounds, the pattern matrix method. Specifically, fix an arbitrary function f:{0,1}^n->{0,1} and let A_f be the matrix whose columns are each an application of f to some…
This article investigates the exploitation of semantic communications in multi-user networks. We propose a novel heterogeneous semantic and bit multi-user framework for providing flawless, customized, and intelligent information…
For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In…
We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…
In this note, we study the relation between the parity decision tree complexity of a boolean function $f$, denoted by $\mathrm{D}_{\oplus}(f)$, and the $k$-party number-in-hand multiparty communication complexity of the XOR functions…
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…
In order to meet the demands of future innovative applications, many efforts have been made to exceed the limits predicted by Shannon's Theory. Besides the investigation of beyond-Shannon metrics such as security, latency, and semantics,…
One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially…
We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function $f(x,y)$ of their inputs by sending polynomial-size messages to a computationally bounded…
We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for…
Deterministic and probabilistic communication protocols are introduced in which parties can exchange the values of polynomials (rather than bits in the usual setting). It is established a sharp lower bound $2n$ on the communication…
Network calculus is often used to prove delay bounds in deterministic networks, using arrival and service curves. We consider a FIFO system that offers a rate-latency service curve and where packet transmission occurs at line rate without…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of…
Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…
We consider the problem of zero-error function computation with side information. Alice and Bob have correlated sources $X,Y$ with joint p.m.f. $p_{XY}(\cdot, \cdot)$. Bob wants to calculate $f(X,Y)$ with zero error. Alice encodes…
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…
We exhibit an $n$-bit communication problem with a constant-cost randomized protocol but which requires $n^{\Omega(1)}$ deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized…
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently,…