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机制具有更高的吞吐量，且能耗较低。此外，其现代实现融合了个性化与异质性信任特征，正逐步成为全球金融基础设施的理想候选方案。然而，由于不同进程的仲裁集合不再统一，这些系统为支持可靠广播和共识等抽象机制所需维持的性质尚未得到充分理解。本文首先构建了一个通用的异质仲裁系统模型，允许每个参与者自行声明其仲裁集合，并归纳其特性。已有研究表明仲裁交集性与可用性两项性质是必要条件，但本文证明了二者并不构成充分条件。随后我们定义了仲裁包含性概念，并证明三个条件共同构成充分条件：通过提出可靠广播与共识协议，我们验证了满足这三项性质的仲裁系统在协议正确性方面的有效性。