We present the notion of a multilevel, slashable quorum system, where an application can obtain gradual levels of assurance that a certain value is bound to be decided (or "finalized") in a global consensus procedure, unless a large number of Byzantine processes are exposed to slashing (that is, penalty on staked assets). Our construction is a highly parameterized generalization of quorum systems based on finite projective spaces, with asymptotic high availability and optimal slashing properties. In particular, we show that any quorum system whose ground elements are disjoint subsets of nodes (e.g. "commmittees" in committee-based consensus protocols) has asymptotic high availability under very reasonable conditions, a general proof with significance of its own. Under similarly relaxed conditions, we show that our construction has asymptotically optimal slashing properties with respect to message complexity and process load; this illustrates a fundamental trade off between message complexity, load, and slashing. Our multilevel construction allows nodes to decide how many "levels" of finalization assurance they wish to obtain, noting that this functionality, if applied to a proof-of-stake blockchain, can be seen either as (i) a form of an early, slashing-based, probabilistic block finalization; or (ii) a service for reorg tolerance.

翻译：我们提出了多级可罚没仲裁系统的概念，其中应用可获得渐进的保证级别，即某个值必然会在全局共识过程中被决定（或"最终确定"），除非大量拜占庭进程暴露于罚没（即对质押资产的惩罚）。我们的构造是基于有限射影空间的仲裁系统的高度参数化泛化，具有渐近高可用性和最优罚没特性。特别地，我们证明任何基础元素为节点不相交子集（例如基于委员会的共识协议中的"委员会"）的仲裁系统，在非常合理的条件下具有渐近高可用性——这一通用证明本身具有重要意义。在同样宽松的条件下，我们证明我们的构造在消息复杂度和进程负载方面具有渐近最优罚没特性；这揭示了消息复杂度、负载与罚没之间的基本权衡。我们的多级构造允许节点决定希望获得多少"级别"的最终确认保证，注意到这一功能若应用于权益证明区块链，可被视为（i）一种基于罚没的早期概率性区块最终确认形式；或（ii）一种重组容错服务。