Byzantine quorum systems provide higher throughput than proofof-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. In this paper, we first see a general model of heterogeneous quorum systems where each participant can declare its own quorums, and capture their properties. 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 inclusion, 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.

翻译：拜占庭仲裁系统相比工作量证明具有更高的吞吐量，且能耗适中。此外，其现代实现融合了个性化与非均匀信任机制，正逐渐成为全球金融基础设施的理想候选方案。然而，由于此类系统的仲裁集合不再在各进程间保持统一，其应具备哪些性质以支撑可靠广播与共识等抽象机制尚不明确。本文首先构建异构仲裁系统的一般模型，允许每个参与者自定义仲裁集合并刻画其性质。已有研究证明仲裁交集性与可用性两个性质不可或缺，但本文进一步证明二者并非充分条件。为此我们提出仲裁包含性概念，并证明这三个条件共同构成充分条件：本文给出可靠广播与共识协议，并证明其在满足这三项性质的仲裁系统中的正确性。