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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 prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact…
In this paper, a communication-efficient multi-processor compressed sensing framework based on the approximate message passing algorithm is proposed. We perform lossy compression on the data being communicated between processors, resulting…
Information distance can be defined not only between two strings but also in a finite multiset of strings of cardinality greater than two. We give an elementary proof for expressing the information distance in terms of plain Kolmogorov…
Individuals, despite having varied life experiences and learning processes, can communicate effectively through languages. This study aims to explore the efficiency of language as a communication medium. We put forth two specific…
In this paper, we analyze the monotone space of complexity of directed connectivity for a large class of input graphs $G$ using the switching network model. The upper and lower bounds we obtain are a significant generalization of previous…
We formulate a model for intermittent communication that can capture bursty transmissions or a sporadically available channel, where in either case the receiver does not know a priori when the transmissions will occur. Focusing on the…
We show lower bounds of $\Omega(\sqrt{n})$ and $\Omega(n^{1/4})$ on the randomized and quantum communication complexity, respectively, of all $n$-variable read-once Boolean formulas. Our results complement the recent lower bound of…
We exhibit a total search problem with classically verifiable solutions whose communication complexity in the quantum SMP model is exponentially smaller than in the classical two-way randomized model. Our problem is a bipartite version of a…
The single-letter characterisation of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
We consider the communication complexity of fundamental longest common prefix (Lcp) problems. In the simplest version, two parties, Alice and Bob, each hold a string, $A$ and $B$, and we want to determine the length of their longest common…
There is growing interest in studying the languages that emerge when neural agents are jointly trained to solve tasks requiring communication through a discrete channel. We investigate here the information-theoretic complexity of such…
Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical…
Eliciting cooperation in multi-agent LLM systems is critical for AI alignment. We investigate two approaches: direct communication and curriculum learning. In a 4-player Stag Hunt, a one-word "cheap talk" channel increases cooperation from…
In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…
In this paper we present a rudimentary model for low-latency anonymous communication systems. Specifically, we study distributed OR algorithm as an abstract of the system. Based on our model, we give several satisfactory lower bounds of…
We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing,…
We provide a lower bound on the expected discovery time of one-way neighbor discovery in multi antenna system. We assume that the scheme allows to use different directional transmission probabilities, which result in different probability…
Consensus is one of the most thoroughly studied problems in distributed computing, yet there are still complexity gaps that have not been bridged for decades. In particular, in the classical message-passing setting with processes' crashes,…