Unbeatable Consensus

Castañeda, Armando; Gonczarowski, Yannai A.; Moses, Yoram

doi:10.1007/978-3-662-45174-8_7

Cited by 18 publications

(33 citation statements)

References 23 publications

(55 reference statements)

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“…Related work. Work on knowledge and distributed systems is of course one of the inspirations of the present work [26], especially where connectivity [7,8] is used. But the authors know of no previous work using DEL [4,10] to study such systems, and neither on directly connecting the combinatorial topological setting of [16] with Kripke models.…”

Section: Introductionmentioning

confidence: 99%

A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

Goubault

Ledent

Rajsbaum

2018

Electron. Proc. Theor. Comput. Sci.

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The usual epistemic S5 n model for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in this structure, by considering a dual, simplicial complex model. We use dynamic epistemic logic (DEL) to study how an epistemic simplicial complex model changes after a set of agents communicate with each other. We concentrate on an action model that represents the so-called immediate snapshot communication patterns of asynchronous agents, because it is central to distributed computability (but our setting works for other communication patterns). There are topological invariants preserved from the initial epistemic complex to the one after the action model is applied, which determine the knowledge that the agents gain after communication. Finally, we describe how a distributed task specification can be modeled as a DEL action model, and show that the topological invariants determine whether the task is solvable. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.

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Section: Introductionmentioning

confidence: 99%

A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

Goubault

Ledent

Rajsbaum

2018

Electron. Proc. Theor. Comput. Sci.

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“…The correctness proof of the algorithm is shown in [3]. The validity and termination properties are easy to prove.…”

Section: An Algorithm Based Onmentioning

confidence: 99%

“…The predicate P pref0 , introduced in [3], allows processes to decide as soon as possible on a preferred value, 0 in this case, while the other value 1 is decided only when the process is sure that no process decides on the preferred value 0. The predicate is expressed in the knowledge-based approach in distributed computing, in the spirit of [9].…”

Section: P Pref0 (P 3 ): a Knowledge-based Unbeatable Predicatementioning

confidence: 99%

“…Let ∃ correct 0(i, r) denote the predicate: "p i knows that at least one correct process knows in round r that there is a 0" and let ∃ revealed(i, r) denote the predicate: "a round r ≤ r has been revealed to p i ". The early deciding/stopping predicate P 3 = P pref0 is defined as [3]:…”

Section: P Pref0 (P 3 ): a Knowledge-based Unbeatable Predicatementioning

confidence: 99%

“…3 contains the early deciding/stopping consensus algorithm based on P pref0 , introduced in [3]. The processes proceed in a sequence of synchronous rounds (the variable r denotes the current round).…”

Section: An Algorithm Based Onmentioning

confidence: 99%

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Early Decision and Stopping in Synchronous Consensus: A Predicate-Based Guided Tour

Castañeda¹,

Moses

Raynal

et al. 2017

Lecture Notes in Computer Science

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Abstract. Consensus is the most basic agreement problem encountered in faulttolerant distributed computing: each process proposes a value and non-faulty processes must agree on the same value, which has to be one of the proposed values. While this problem is impossible to solve in asynchronous systems prone to process crash failures, it can be solved in synchronous (round-based) systems where all but one process might crash in any execution. It is well-known that (t + 1) rounds are necessary and sufficient in the worst case execution scenario for the processes to decide and stop executing, where t < n is a system parameter denoting the maximum number of allowed process crashes and n denotes the number of processes in the system. Early decision and stopping considers the case where f < t processes actually crash, f not being known by processes. It has been shown that the number of rounds that have to be executed in the worst case is then min(f + 2, t + 1). Following Castañeda, Gonczarowski and Moses (DISC 2014), the paper shows that this value is an upper bound attained only in worst execution scenarios. To this end, it investigates a sequence of three early deciding/stopping predicates P1 = Pcount, P2 = P dif and P3 = P pref0 , of increasing power, which differ in the information obtained by the processes from the actual failure, communication and data pattern. It is shown that each predicate Pi is better than the previous one Pi−1, i ∈ {2, 3}, in the sense that there are executions where Pi allows processes to reach a decision earlier than Pi−1, while Pi−1 never allows a process to decide earlier than Pi. Moreover, P3 = P pref0 is an unbeatable predicate in the sense that it cannot be strictly improved: if there is an early deciding/stopping predicate P that improves the decision time of a process with respect to P pref0 in a given execution, then there is at least one execution in which a process decides with P strictly later than with P pref0 .

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