We write down a formal framework for the analysis of both permissioned and permissionless systems. Within this framework, we then consider the Byzantine Generals Problem as a formalisation of the problem of reaching consensus, and address a programme of research that asks, "Under what adversarial conditions, and for what types of permissionless protocol, is consensus possible?" We prove a number of results for this programme, our main result being that deterministic consensus is not possible for decentralised permissionless protocols. To close, we give a list of seven open questions.

翻译：我们为分析有许可和无许可的系统制定了一个正式框架。在此框架内,我们随后将拜占庭将军问题视为正式解决达成共识的问题,并处理一项研究方案,该方案要求“在何种对抗条件下,以及对于何种类型的无许可议定书,可以达成共识?” 我们证明这个方案取得了一些成果,我们的主要结果是,无法就无许可的分散协议达成决定性的共识。最后,我们提出七个未决问题清单。