Related papers: Communication Complexities of XOR functions
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…
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 develop a novel connection between discrepancy minimization and (quantum) communication complexity. As an application, we resolve a substantial special case of the Matrix Spencer conjecture. In particular, we show that for every…
We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwise comparisons. For…
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
We show that the unrestricted black-box complexity of the $n$-dimensional XOR- and permutation-invariant LeadingOnes function class is $O(n \log (n) / \log \log n)$. This shows that the recent natural looking $O(n\log n)$ bound is not…
We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$. For arbitrary functions, we obtain lower bounds and…
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…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
Communication complexity quantifies how difficult it is for two distant computers to evaluate a function f(X,Y), where the strings X and Y are distributed to the first and second computer respectively, under the constraint of exchanging as…
A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired…
$\newcommand{\F}{\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\F_2^n\to \{0,1\}$, and $A=Mx+b$ for $M…
We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting optimal constant factors in the leading terms in a number of different models. In…
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…
In this work we give an example of exponential separation between quantum and classical resources in the setting of XOR games assisted with communication. Specifically, we show an example of a XOR game for which $O(n)$ bits of two way…
The minimal Kolmogorov complexity of a total computable function that exceeds everywhere all total computable functions of complexity at most $n$, is $2^{n+O(1)}$. If we replace "everywhere" by "for all sufficiently large inputs", the…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with and without help…
We obtain a lower bound of n^Omega(1) on the k-party randomized communication complexity of the Disjointness function in the `Number on the Forehead' model of multiparty communication when k is a constant. For k=o(loglog n), the bounds…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…