Reachability and Expectation in Gossiping

Ditmarsch, Hans van; Kokkinis, Ioannis; Stockmarr, Anders

doi:10.1007/978-3-319-69131-2_6

Cited by 13 publications

(12 citation statements)

References 19 publications

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“…For some of the combinations of the parameters the minimum number of calls needed to reach the final situation is established. The expected time of termination of several gossip protocols on completely connected networks was studied by van Ditmarsch, Kokkinis, and Stockmarr (2017a).…”

Section: Related Workmentioning

confidence: 99%

Verification of Distributed Epistemic Gossip Protocols

Apt¹,

Wojtczak²

2018

jair

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Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Distributed epistemic gossip protocols use as guards formulas from a simple epistemic logic and as statements calls between the agents. They are natural examples of knowledge based programs.We prove here that these protocols are implementable, that their partial correctness is decidable and that termination and two forms of fair termination of these protocols are decidable, as well. To establish these results we show that the definition of semantics and of truth of the underlying logic are decidable.

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Section: Related Workmentioning

confidence: 99%

Verification of Distributed Epistemic Gossip Protocols

Apt¹,

Wojtczak²

2018

jair

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“…. In the long run this does not matter: the expected execution of ANY is in the order of n log n [5,12,21], and this is also the case for LNS and for yet other protocols considered in this work [23].…”

Section: Introductionmentioning

confidence: 76%

Dynamic Gossip

Ditmarsch

Eijck

Pardo

et al. 2018

Bull. Iran. Math. Soc.

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A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. The goal is for all agents to get to know all secrets, in which case we call the execution of the protocol successful. We consider distributed and dynamic gossip protocols. In distributed gossip the agents themselves instead of a global scheduler determine whom to call. In dynamic gossip not only secrets are exchanged but also telephone numbers (agent identities). This results in increased graph connectivity. We define six such distributed dynamic gossip protocols, and we characterize them in terms of the topology of the graphs on which they are successful, wherein we distinguish strong success (the protocol always terminates, possibly assuming fair scheduling) from weak success (the protocol sometimes terminates). For five of these protocols strong (fair) and weak success are characterized by weakly connected graphs. This result is surprising because the protocols are fairly different. In the sixth protocol an agent may only call another agent if it does not know the other agent's secret. Strong success for this protocol is characterized by graphs for which the set of non-terminal nodes is strongly connected. Weak success for this protocol is characterized by weakly connected graphs satisfying further topological constraints that we define in the paper. One direction of this characterization is surprisingly harder to prove than the other results in this contribution.

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“…Furthermore, they are strongly successful, i.e., they are guaranteed to terminate and to turn all agents into experts. Unfortunately, they are not very fast: both HMS and LNS require, in the worst case, quadratically many calls, and are likely to have the same the n log n expectation as the protocol of just making random calls [32,38]. It is unclear whether we can do substantially better than an n log n expected termination, but it seems conceivable that more efficient epistemic protocols might result by exploiting the specific properties of knowledge in gossip protocols.…”

Section: The Gossip Problemmentioning

confidence: 99%

The logic of gossiping

Ditmarsch¹,

Hoek²,

Kuijer³

2020

Artificial Intelligence

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The so-called gossip problem is a formal model of peer-to-peer communication. In order to perform such communication efficiently, it is important to keep track of what agents know about who holds what information at a given point in time. The knowledge that the agents possess depends strongly on the particular type of communication that is used. Here, we formally define a large number of different variants of the gossip problem, that differ in the extent to which communication is private (observable, synchronous or asynchronous), the direction of the flow of information (caller to callee, callee to caller or both) and whether the agents become aware of the exact set of information possessed by their communication partner. We consider a number of formulas that represent interesting properties that a gossip situation may or may not enjoy, and show for which variants they are valid. Additionally, we show that the model checking and validity checking problems for each variant are decidable, and we introduce sound and complete proof systems for them.

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Reachability and Expectation in Gossiping

Cited by 13 publications

References 19 publications

Verification of Distributed Epistemic Gossip Protocols

Verification of Distributed Epistemic Gossip Protocols

Dynamic Gossip

The logic of gossiping

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