Synchronous t-Resilient Consensus in Arbitrary Graphs

Castañeda, Armando; Fraigniaud, Pierre; Paz, Ami; Rajsbaum, Sergio; Roy, Matthieu; Travers, Corentin

doi:10.1007/978-3-030-34992-9_5

Cited by 7 publications

(2 citation statements)

References 34 publications

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“…Many technical interesting issues arise, such as defining morphisms between complexes, understanding the relation between belief and a dead agent, but the main point is that our work opens the way to give a formal epistemic semantics to distributed systems where processes may fail and failures are detectable (as in the synchronous crash failure model). It would be interesting to use our simplicial model to reason about the solvability of tasks in such systems, for example, the following have not been studied using epistemic logic, to the best of our knowledge: non-complete communication (instead of broadcast situation we considered here) graphs [4], renaming [28], and lattice agreement [36].…”

Section: Discussionmentioning

confidence: 99%

A Simplicial Model for $KB4_n$: Epistemic Logic with Agents that May Die

Goubault¹,

Ledent²,

Rajsbaum³

2021

Preprint

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The standard semantics of multi-agent epistemic logic S5n is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that has been formalized as pure simplicial models in [13]. Here we extend the theory to encompass all simplicial models -including the ones that are not pure. The corresponding Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. This yields the epistemic logic KB4n, which can reason about situations where some of the agents may die.

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Section: Discussionmentioning

confidence: 99%

A Simplicial Model for $KB4_n$: Epistemic Logic with Agents that May Die

Goubault¹,

Ledent²,

Rajsbaum³

2021

Preprint

Self Cite

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“…In a related work, Choudhury et al [18] provided a time-optimal algorithm to solve Consensus in directed graphs with node crashes. Castañeda et al [8] considered networks with nodes prone to crashes with an upper bound t on the number of crashes and showed that, as long at the network remained (t + 1)-connected, Consensus was solvable in a number of rounds determined by how conducive the network was to broadcasting. Chlebus et al [15] studied networks with Byzantine nodes such that the removal of faulty nodes leaves a network that is sufficiently connected; they gave fast solutions to Consensus and showed a separation of Consensus with Byzantine nodes from Consensus with Byzantine nodes using message authentication, with respect to asymptotic time performance in suitably connected networks.…”

Section: Introductionmentioning

confidence: 99%

Consensus in Networks Prone to Link Failures

Chlebus¹,

Kowalski²,

Olkowski³

et al. 2021

Preprint

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We consider deterministic distributed algorithms solving Consensus in synchronous networks of arbitrary topologies. Links are prone to failures. Agreement is understood as holding in each connected component of a network obtained by removing faulty links. We introduce the concept of stretch, which is a function of the number of connected components of a network and their respective diameters. Fast and early-stopping algorithms solving Consensus are defined by referring to stretch resulting in removing faulty links. We develop algorithms that rely only on nodes knowing their own names and the ability to associate communication with local ports. A network has n nodes and it starts with m functional links. We give a general algorithm operating in time n that uses messages of O(log n) bits. If we additionally restrict executions to be subject to a bound Λ on stretch, then there is a fast algorithm solving Consensus in time O(Λ) using messages of O(log n) bits. Let λ be an unknown stretch occurring in an execution; we give an algorithm working in time (λ + 2) 3 and using messages of O(n log n) bits. We show that Consensus can be solved in the optimal O(λ) time, but at the cost of increasing message size to O(m log n). We also demonstrate how to solve Consensus by an algorithm that uses only O(n) non-faulty links and works in time O(nm), while nodes start with their ports mapped to neighbors and messages carry O(m log n) bits. We prove lower bounds on performance of Consensus solutions that refer to parameters of evolving network topologies and the knowledge available to nodes.

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