Dynamic Gossip

Ditmarsch, Hans van; Eijck, Jan van; Pardo, Pere; Ramezanian, Rahim; Schwarzentruber, François

doi:10.1007/s41980-018-0160-4

Cited by 10 publications

(36 citation statements)

References 22 publications

(52 reference statements)

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“…They differ from the ones here considered, which are static. This set up was further investigated in [15] where various dynamic gossip protocols were proposed and analyzed. In [19] such protocols were analyzed by embedding them in a network programming language NetKAT proposed in [1].…”

Section: Related Workmentioning

confidence: 99%

Open Problems in a Logic of Gossips

Apt

Wojtczak

2019

Electron. Proc. Theor. Comput. Sci.

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Gossip protocols are programs used in a setting in which each agent holds a secret and the aim is to reach a situation in which all agents know all secrets. Such protocols rely on a point-to-point or group communication. Distributed epistemic gossip protocols use epistemic formulas in the component programs for the agents. The advantage of the use of epistemic logic is that the resulting protocols are very concise and amenable for a simple verification.Recently, we introduced a natural modal logic that allows one to express distributed epistemic gossip protocols and to reason about their correctness. We proved that the resulting protocols are implementable and that all aspects of their correctness, including termination, are decidable. To establish these results we showed that both the definition of semantics and of truth of the underlying logic are decidable. We also showed that the analogous results hold for an extension of this logic with the 'common knowledge' operator.However, several, often deceptively simple, questions about this logic and the corresponding gossip protocols remain open. The purpose of this paper is to list and elucidate these questions and provide for them an appropriate background information in the form of partial of related results.

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Section: Related Workmentioning

confidence: 99%

Open Problems in a Logic of Gossips

Apt

Wojtczak

2019

Electron. Proc. Theor. Comput. Sci.

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“…for any P 1 and P 2 from the five protocols. It is interesting that although all five protocols can reach the final distribution on complete graphs [5], their reachability strength on intermediate distributions varies.…”

Section: Reachabilitymentioning

confidence: 99%

“…In [1] the focus is on distributed gossip, including information change in one direction only, and termination. The extension (permitted call sequences of the protocols) and the characterization of the classes of graphs where the (dynamic versions) of our protocols terminate were investigated in [5], where their main result is for LNS (in [9] the same question was answered for the (static) protocol CO). In [2,3] the focus is on the logical dynamics of call exchange.…”

Section: Introductionmentioning

confidence: 99%

Reachability of Five Gossip Protocols

Ditmarsch¹,

Gattinger²,

Kokkinis³

et al. 2019

Lecture Notes in Computer Science

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Gossip protocols use point-to-point communication to spread information within a network until every agent knows everything. Each agent starts with her own piece of information ('secret') and in each call two agents will exchange all secrets they currently know. Depending on the protocol, this leads to different distributions of secrets among the agents during its execution. We investigate which distributions of secrets are reachable when using several distributed epistemic gossip protocols from the literature. Surprisingly, a protocol may reach the distribution where all agents know all secrets, but not all other distributions. The five protocols we consider are called ANY, LNS, CO, TOK, and SPI. We find that TOK and ANY reach the same distributions but all other protocols reach different sets of distributions, with some inclusions. Additionally, we show that all distributions are subreachable with all five protocols: any distribution can be reached, if there are enough additional agents.

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“…Dynamic gossip from [7] is another variation of the problem: not only is there a reachability graph restricting who can call whom, but this graph is also manipulated when phone calls are made. Intuitively, the agents now also exchange phone numbers, in addition to the secrets.…”

Section: Dynamic Gossipmentioning

confidence: 99%

“…We leave the more interesting and challenging task as future work: to actually find these algebraic proofs. Moreover, it would be interesting to find a proof on the meta-level by working with schemata of Netkat expressions instead of a specific G. This could yield a completely new proof of Theorem 2 or one can try to translate the proof from [7] to Netkat.…”

Section: Theorem 6 (Sun Graphs In Netkatmentioning

confidence: 99%

Towards an Analysis of Dynamic Gossip in Netkat

Gattinger

Wagemaker

2018

Relational and Algebraic Methods in Computer Science

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In this paper we analyse the dynamic gossip problem using the algebraic network programming language Netkat. Netkat is a language based on Kleene algebra with tests and describes packets travelling through networks. It has a sound and complete axiomatisation and an efficient coalgebraic decision procedure. Dynamic gossip studies how information spreads through a peer-to-peer network in which links are added dynamically. In this paper we embed dynamic gossip into Netkat. We show that a reinterpretation of Netkat in which we keep track of the state of switches allows us to model Learn New Secrets, a well-studied protocol for dynamic gossip. We axiomatise this reinterpretation of Netkat and show that it is sound and complete with respect to the packet-processing model, via a translation back to standard Netkat. Our main result is that many common decision problems about gossip graphs can be reduced to checks of Netkat equivalences. We also implemented the reduction.

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Dynamic Gossip

Cited by 10 publications

References 22 publications

Open Problems in a Logic of Gossips

Open Problems in a Logic of Gossips

Reachability of Five Gossip Protocols

Towards an Analysis of Dynamic Gossip in Netkat

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