A set of mutually distrusting participants that want to agree on a common opinion must solve an instance of a Byzantine agreement problem. These problems have been extensively studied in the literature. However, most of the existing solutions assume that the participants are aware of $n$ -- the total number of participants in the system -- and $f$ -- an upper bound on the number of Byzantine participants. In this paper, we show that most of the fundamental agreement problems can be solved without affecting resiliency even if the participants do not know the values of (possibly changing) $n$ and $f$. Specifically, we consider a synchronous system where the participants have unique but not necessarily consecutive identifiers, and give Byzantine agreement algorithms for reliable broadcast, approximate agreement, rotor-coordinator, early terminating consensus and total ordering in static and dynamic systems, all with the optimal resiliency of $n> 3f$. Moreover, we show that synchrony is necessary as an agreement with probabilistic termination is impossible in a semi-synchronous or asynchronous system if the participants are unaware of $n$ and $f$.

中文翻译：

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与未知参与者的拜占庭协议和失败

一组希望达成共识的相互不信任的参与者必须解决一个拜占庭协议问题的实例。这些问题已在文献中进行了广泛研究。但是，大多数现有解决方案都假定参与者知道$ n $（系统中参与者的总数）和$ f $（拜占庭参与者的数量上限）。在本文中，我们表明即使参与者不知道（可能会改变）$ n $和$ f $的值，也可以在不影响弹性的情况下解决大多数基本协议问题。具体来说，我们考虑一个参与者拥有唯一但不一定是连续标识符的同步系统，并给出用于可靠广播的拜占庭协议算法，近似协议，转子协调器，在静态和动态系统中尽早终止共识和总排序，所有这些都具有$ n> 3f $的最佳弹性。此外，我们显示出同步是必要的，因为如果参与者不知道$ n $和$ f $，则在半同步或异步系统中不可能与概率终止达成协议。