Quorum Subsumption for Heterogeneous Quorum Systems

Authors Xiao Li, Eric Chan, Mohsen Lesani

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Xiao Li
  • University of California, Riverside, CA, USA
Eric Chan
  • University of California, Riverside, CA, USA
Mohsen Lesani
  • University of California, Riverside, CA, USA


We would like to thank DISC '23 reviewers for detailed and constructive reviewers. Further, we would like to specially thank Giuliano Losa for his insightful comments.

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Xiao Li, Eric Chan, and Mohsen Lesani. Quorum Subsumption for Heterogeneous Quorum Systems. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Byzantine quorum systems provide higher throughput than proof-of-work and incur modest energy consumption. Further, their modern incarnations incorporate personalized and heterogeneous trust. Thus, they are emerging as an appealing candidate for global financial infrastructure. However, since their quorums are not uniform across processes anymore, the properties that they should maintain to support abstractions such as reliable broadcast and consensus are not well-understood. It has been shown that the two properties quorum intersection and availability are necessary. In this paper, we prove that they are not sufficient. We then define the notion of quorum subsumption, and show that the three conditions together are sufficient: we present reliable broadcast and consensus protocols, and prove their correctness for quorum systems that provide the three properties.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
  • Computer systems organization → Availability
  • Computer systems organization → Reliability
  • Distributed Systems
  • Impossibility Results
  • Byzantine fault tolerance


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