research-article

Programming simultaneous actions using common knowledge

Authors:

Mark R. TuttleAuthors Info & Claims

Algorithmica, Volume 3, Issue 1-4

Pages 121 - 169

https://doi.org/10.1007/BF01762112

Published: 01 November 1988 Publication History

Abstract

This work applies the theory of knowledge in distributed systems to the design of efficient fault-tolerant protocols. We define a large class of problems requiring coordinated, simultaneous action in synchronous systems, and give a method of transforming specifications of such problems into protocols that areoptimal in all runs: these protocols are guaranteed to perform the simultaneous actions as soon as any other protocol could possibly perform them, given the input to the system and faulty processor behavior. This transformation is performed in two steps. In the first step we extract, directly from the problem specification, a high-level protocol programmed using explicit tests for common knowledge. In the second step we carefully analyze when facts become common knowledge, thereby providing a method of efficiently implementing these protocols in many variants of the omissions failure model. In the generalized omissions model, however, our analysis shows that testing for common knowledge is NP-hard. Given the close correspondence between common knowledge and simultaneous actions, we are able to show that no optimal protocol for any such problem can be computationally efficient in this model. The analysis in this paper exposes many subtle differences between the failure models, including the precise point at which this gap in complexity occurs.

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Cited By

Humml MSchröder LWilliams BChen YNeville J(2023)Common knowledge of abstract groupsProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i5.25791(6434-6441)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i5.25791
Alpturer KHalpern Jvan der Meyden ROshman RNolin AHalldorsson MBalliu A(2023)Optimal Eventual Byzantine Agreement Protocols with Omission FailuresProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594573(244-252)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594573
Cignarale GSchmid UTahko TKuznets R(2023)The Role of A Priori Belief in the Design and Analysis of Fault-Tolerant Distributed SystemsMinds and Machines10.1007/s11023-023-09631-333:2(293-319)Online publication date: 17-Apr-2023
https://dl.acm.org/doi/10.1007/s11023-023-09631-3
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Published In

cover image Algorithmica

Algorithmica Volume 3, Issue 1-4

Nov 1988

559 pages

ISSN:0178-4617

Issue’s Table of Contents

© Springer-Verlag New York Inc. 1988.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 November 1988

Revision received: 20 May 1987

Received: 11 November 1986

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Cited By

Humml MSchröder LWilliams BChen YNeville J(2023)Common knowledge of abstract groupsProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i5.25791(6434-6441)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i5.25791
Alpturer KHalpern Jvan der Meyden ROshman RNolin AHalldorsson MBalliu A(2023)Optimal Eventual Byzantine Agreement Protocols with Omission FailuresProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594573(244-252)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594573
Cignarale GSchmid UTahko TKuznets R(2023)The Role of A Priori Belief in the Design and Analysis of Fault-Tolerant Distributed SystemsMinds and Machines10.1007/s11023-023-09631-333:2(293-319)Online publication date: 17-Apr-2023
https://dl.acm.org/doi/10.1007/s11023-023-09631-3
Castañeda AGonczarowski YMoses Y(2022)Unbeatable consensusDistributed Computing10.1007/s00446-021-00417-335:2(123-143)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00446-021-00417-3
Fitzi MLiu-Zhang CLoss JMiller ACensor-Hillel K(2021)A New Way to Achieve Round-Efficient Byzantine AgreementProceedings of the 2021 ACM Symposium on Principles of Distributed Computing10.1145/3465084.3467907(355-362)Online publication date: 21-Jul-2021
https://dl.acm.org/doi/10.1145/3465084.3467907
Schlögl TSchmid UKuznets R(2020)The Persistence of False Memory: Brain in a Vat Despite Perfect ClocksPRIMA 2020: Principles and Practice of Multi-Agent Systems10.1007/978-3-030-69322-0_30(403-411)Online publication date: 18-Nov-2020
https://dl.acm.org/doi/10.1007/978-3-030-69322-0_30
Fruzsa K(2019)Hope for Epistemic Reasoning with Faulty Agents!Selected Reflections in Language, Logic, and Information10.1007/978-3-031-50628-4_6(93-108)Online publication date: 5-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-031-50628-4_6
Kuznets RProsperi LSchmid UFruzsa K(2019)Epistemic Reasoning with Byzantine-Faulty AgentsFrontiers of Combining Systems10.1007/978-3-030-29007-8_15(259-276)Online publication date: 4-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-29007-8_15
Castañeda AGonczarowski YMoses YGiakkoupis G(2016)Unbeatable Set Consensus via Topological and Combinatorial ReasoningProceedings of the 2016 ACM Symposium on Principles of Distributed Computing10.1145/2933057.2933120(107-116)Online publication date: 25-Jul-2016
https://dl.acm.org/doi/10.1145/2933057.2933120
Halpern JMoses Y(2014)A procedural characterization of solution concepts in gamesJournal of Artificial Intelligence Research10.5555/2655713.265571849:1(143-170)Online publication date: 1-Jan-2014
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