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In the wake of the decisive impossibility result of Fischer, Lynch, and Paterson for deterministic consensus protocols in the aynchronous model with just one failure, Ben-Or and Bracha demonstrated that the problem could be solved with…
In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sa\u{g}lam and Tardos and Brody et al. showed…
We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the "data-processing bound," is the simplest and…
We show nearly quadratic separations between two pairs of complexity measures: 1. We show that there is a Boolean function $f$ with $D(f)=\Omega((D^{sc}(f))^{2-o(1)})$ where $D(f)$ is the deterministic query complexity of $f$ and $D^{sc}$…
We demonstrate a deterministic Byzantine consensus algorithm with synchronous operation in partial synchrony. It is naturally leaderless, tolerates any number of $ f<n/2 $ Byzantine processes with 2 rounds of exchange of originator-only…
In this paper we study the data exchange problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets,…
We study the effect that the amount of correlation in a bipartite distribution has on the communication complexity of a problem under that distribution. We introduce a new family of complexity measures that interpolates between the two…
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the…
Quantum Byzantine Agreement (QBA), a cornerstone of quantum blockchain, offers inherent advantages in security and fault tolerance over classical protocols, guaranteed by the laws of quantum mechanics. However, existing multiparty QBA…
We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical…
In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label "$+$" or "$-$" to…
We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs: * testing if an undirected graph has a perfect matching (this implies lower…
State redistribution is the protocol in which, given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
This paper presents a novel leaderless protocol (FPC-BI: Fast Probabilistic Consensus within Byzantine Infrastructures) with a low communicational complexity and which allows a set of nodes to come to a consensus on a value of a single bit.…
We provide tight upper and lower bounds on the noise resilience of interactive communication over noisy channels with feedback. In this setting, we show that the maximal fraction of noise that any robust protocol can resist is 1/3.…
In agreement problems, each process has an input value and must choose a decision (output) value. Given $n\geq 2$ processes and $m \geq 2$ possible different input values, we want to design an agreement algorithm that enables as many…
A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian agents with common priors will never "agree to disagree": if their opinions about any topic are common knowledge, then those opinions must be equal. Economists have…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
We consider the class of functions whose value depends only on the intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class there is an f_F: 2^{[n]} \to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1 \cap X_2 \cap ...…