一路向下的对称性
Symmetry all the way down
AI总结：
研究不对称信任能否解决分布式任务及具体情况，借助深度层次结构，证明其不增加深度二及以上任务的可解性，通过编译器转换系统展示结果，还证明该结果在深度层次中是紧密的。
摘要：
不对称信任通过允许每个进程指定自己的故障假设来推广经典对称仲裁系统。虽然这种灵活性能够容忍更多故障场景，但尚不清楚在这些情况下是否真的可以解决分布式任务以及能解决哪些任务。我们使用不对称信任的深度层次结构来回答这个问题，证明不对称信任不会增加需要深度二或更高的任务的可解性。具体而言，对于任何拜占庭不对称仲裁系统，任何允许解决需要深度至少为二的任务的故障场景也可以被适当构造的拜占庭对称仲裁系统容忍。我们通过一个将不对称仲裁系统转换为对称仲裁系统的编译器来展示这一点。不对称信任专门容忍的额外故障模式对应于只能解决需要深度一或更低的更简单任务（如一致广播）的场景。我们进一步证明这个结果在深度层次中是紧密的，即不存在在正确进程深度为一或更低的故障场景中也有效的产生对称仲裁系统的编译器。我们的结果阐明了不对称信任的确切能力。虽然它严格扩大了可容忍故障模式的集合，但它并没有为解决需要深度二或更高的任务提供额外的能力。
英文摘要：
Asymmetric trust generalizes classical symmetric quorum systems by allowing each process to specify its own failure assumptions. While this flexibility enables tolerance of strictly more failure scenarios, it is not known if, in these cases, it is actually possible to solve distributed tasks, and if so, which. We answer this question using the depth hierarchy for asymmetric trust (Amores-Sesar et al., OPODIS~'25), which characterizes how much a process must rely on others to solve a task. We prove that asymmetric trust does not increase the solvability of tasks requiring depth two or more, such as reliable broadcast or consensus. Specifically, for any Byzantine asymmetric quorum system, every failure scenario that permits solving a task requiring depth at least two can also be tolerated by a suitably constructed Byzantine symmetric quorum system. We show this via a compiler that transforms asymmetric quorum systems into symmetric ones. The additional failure patterns tolerated exclusively by asymmetric trust correspond to scenarios in which only simpler tasks requiring depth one or less (such as consistent broadcast) can be solved. We further prove that this result is tight in the depth hierarchy, meaning that there exist no compilers that produce symmetric quorum systems that are valid also in failure scenarios where correct processes have depths one or less. Our results clarify the precise power of asymmetric trust. While it strictly enlarges the set of tolerable failure patterns, it does not provide additional strength for solving tasks requiring depth two or higher.
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