Information Complexity of the AND Function in the Two-Party and Multi-party Settings

Filmus, Yuval; Hatami, Hamed; Li, Yaqiao; You, Suzin

doi:10.1007/978-3-319-62389-4_17

Cited by 3 publications

(2 citation statements)

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“…Of particular relevance is the recently introduced notion of information complexity [4,15,24,25], which quantifies the amount of information that the communication reveals regarding the inputs of the players to each other, or to an external observer. In [4], Braverman et al showed that the information complexity of the AND function in a two-party multi-round setting, assuming that errors are not allowed, is 1.4923 bits.…”

Section: Related Workmentioning

confidence: 99%

Public Communication can Facilitate Low-Risk Coordination under Surveillance

Korman,

Crescenzi

2021

Preprint

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Consider a sub-population of rebels that wish to initiate a revolution. In order to avoid initializing a failed revolution, rebels would first strive to estimate their relative "power", which is often correlated with their fraction in the population. However, and especially in non-democratic countries, rebels refrain from disclosing themselves. This poses a significant challenge for rebels: estimating their fraction in the population while minimizing the risk of being identified as rebels. This paper introduces a distributed computing framework aiming to study this question. Our main takeaway message is that the communication pattern has a crucial role in achieving such a task. Specifically, we show that relying on the inherent noise in the communication, public communication, characterized by the fact that each message announced by an individual can be viewed by all its neighbors, allows rebels to estimate their fraction in the population while keeping a negligible risk of each rebel being identified as such. The suggested estimation protocol, inspired by historical events, is extremely simple and can be executed covertly even under extreme conditions of surveillance.Conversely, we show that under peer-to-peer communication, protocols of similar simplicity are either inefficient or non-covert. INTRODUCTIONLarge scale changeovers in a population, such as political overthrows of dictatorships by rebels, are often perceived as complex emergent phenomena [9,18,19,34]. In order to avoid conducting a failed rebellion, rebels would typically refrain from initiating a revolution until they manage to obtain a reliable indication that many others will join them [6,30]. In other words, rebels would first try to understand whether "we are the many and they are the few" [33].However, and especially under non-democratic regimes, obtaining such information may not be a trivial task, as rebels often refrain from disclosing themselves as such. In turn, with the lack of such information, the status quo may continue to hold even when the support for a revolution is effectively high. Nevertheless, in some cases, rebels successfully coordinate their actions even under severe conditions of surveillance.Drawing on distributed computing reasoning, we argue that the pattern of communication can play a key role in the ability of rebels to reach such a coordination safely. We distinguish between two extreme patterns in a network environment:• Private communication: Each message sent by an agent is heard by a single neighbor.• Public communication: Each message sent by an agent is heard by all its neighbors. Private communication aims to capture one-to-one interactions, which are executed either directly in person or via a digital private messaging platform. In contrast, public communication aims to model social media infrastructures, such as Facebook or Twitter, that played a significant role during the Arab spring revolutions [19], behavioral communication, such as the "slow-motion" day organized by the opponents of the Pinochet dictator...

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Section: Related Workmentioning

confidence: 99%

Public Communication can Facilitate Low-Risk Coordination under Surveillance

Korman,

Crescenzi

2021

Preprint

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“…The new protocol π might not necessarily have bounded communication, but it will terminate with probability 1. We refer the reader to [15,Signal Simulation Lemma] and [5,Claim 7.14] for more details on such simulations.…”

Section: Information Complexity With Distributional Errormentioning

confidence: 99%

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Dagan¹,

Filmus²,

Hatami³

et al. 2018

Theory of Comput.

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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 ε. • For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order Ω(h(ε)) and O(h(√ ε)), respectively. Here h denotes the binary entropy function. • We analyze the case of the two-bit AND function in detail to show that for this function the gain is Θ(h(ε)). This answers a question of Braverman et al. (STOC'13). • We obtain sharp bounds for the set disjointness function of order n. For the case of the distributional error, we introduce a new protocol that achieves a gain of Θ(h(ε)) provided that n is sufficiently large. We apply these results to answer another question of Braverman et al. regarding the randomized communication complexity of the set disjointness function.

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A Lower Bound for Sampling Disjoint Sets

Göös

Watson

2020

ACM Trans. Comput. Theory

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Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x ⊆ [ n ] and Bob ends up with a set y ⊆ [ n ], such that ( x , y ) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant β < 1, this requires Ω ( n ) communication even to get within statistical distance 1− β n of the target distribution. Previously, Ambainis, Schulman, Ta-Shma, Vazirani, and Wigderson (FOCS 1998) proved that Ω (√ n ) communication is required to get within some constant statistical distance ɛ > 0 of the uniform distribution over all pairs of disjoint sets of size √ n .

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Information Complexity of the AND Function in the Two-Party and Multi-party Settings

Cited by 3 publications

References 9 publications

Public Communication can Facilitate Low-Risk Coordination under Surveillance

Public Communication can Facilitate Low-Risk Coordination under Surveillance

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A Lower Bound for Sampling Disjoint Sets

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