Related papers: Pseudodeterministic Communication Complexity

We present a new method that includes three key components of distributed optimization and federated learning: variance reduction of stochastic gradients, partial participation, and compressed communication. We prove that the new method has…

Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…

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…

In this paper the Neciporuk method for proving lower bounds on the size of Boolean formulae is reformulated in terms of one-way communication complexity. We investigate the scenarios of probabilistic formulae, nondeterministic formulae, and…

We consider the problem of PAC-learning from distributed data and analyze fundamental communication complexity questions involved. We provide general upper and lower bounds on the amount of communication needed to learn well, showing that…

So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…

Set disjointness is a central problem in communication complexity. Here Alice and Bob each receive a subset of an n-element universe, and they need to decide whether their inputs intersect or not. The communication complexity of this…

We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…

Linial's seminal result shows that any deterministic distributed algorithm that finds a $3$-colouring of an $n$-cycle requires at least $\log^*(n)/2 - 1$ communication rounds. We give a new simpler proof of this theorem.

We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…

In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of…

We consider an instance of the following problem: Parties P_1,..., P_k each receive an input x_i, and a coordinator (distinct from each of these parties) wishes to compute f(x_1,..., x_k) for some predicate f. We are interested in one-round…

We study semidefinite relaxations of $\Pi_1$ combinatorial statements. By relaxing the pigeonhole principle, we obtain a new "quantum" pigeonhole principle which is a stronger statement. By relaxing statements of the form "the communication…

We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any…

The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…

Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…

We study the simultaneous message passing (SMP) model of communication complexity, for the case where one party is quantum and the other is classical. We show that in an SMP protocol that computes some function with the first party sending…

We study the following generalized matrix rank estimation problem: given an $n \times n$ matrix and a constant $c \geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is…

We give an exponential separation between one-way quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean Hidden Matching Problem of Bar-Yossef et al.) Earlier such an exponential separation…