Blockchain protocols typically aspire to run in the permissionless setting, in which nodes are owned and operated by a large number of diverse and unknown entities, with each node free to start or stop running the protocol at any time. This setting is more challenging than the traditional permissioned setting, in which the set of nodes that will be running the protocol is fixed and known at the time of protocol deployment. The goal of this paper is to provide a framework for reasoning about the rich design space of blockchain protocols and their capabilities and limitations in the permissionless setting. This paper offers a hierarchy of settings with different "degrees of permissionlessness", specified by the amount of knowledge that a protocol has about the current participants: These are the fully permissionless, dynamically available and quasi-permissionless settings. The paper also proves several results illustrating the utility of our analysis framework for reasoning about blockchain protocols in these settings. For example: (1) In the fully permissionless setting, even with synchronous communication and with severe restrictions on the total size of the Byzantine players, every deterministic protocol for Byzantine agreement has an infinite execution. (2) In the dynamically available and partially synchronous setting, no protocol can solve the Byzantine agreement problem with high probability, even if there are no Byzantine players at all. (3) In the quasi-permissionless and partially synchronous setting, by contrast, assuming a bound on the total size of the Byzantine players, there is a deterministic protocol guaranteed to solve the Byzantine agreement problem in a finite amount of time. (4) In the quasi-permissionless and synchronous setting, every proof-of-stake protocol that does not use advanced cryptography is vulnerable to long-range attacks.

翻译：区块链协议通常旨在无许可环境下运行，在此环境中，节点由大量多样且未知的实体拥有和操作，每个节点可随时自由启动或停止运行协议。该环境比传统的许可环境更具挑战性，后者在协议部署时固定并已知运行协议的节点集合。本文旨在提供一个框架，用于分析区块链协议在无许可环境中的丰富设计空间、能力及局限性。本文提出一个按协议对当前参与者了解程度划分的不同“无许可程度”设置层级结构：完全无许可、动态可用和准无许可环境。本文还证明了若干结果，展示了该分析框架在这些环境中推理区块链协议的实用性。例如：（1）在完全无许可环境中，即使采用同步通信并严格限制拜占庭参与者的总规模，每个用于拜占庭协议的确定性协议都存在无限执行过程。（2）在动态可用且部分同步环境中，即使完全没有拜占庭参与者，任何协议都无法高概率解决拜占庭协议问题。（3）相比之下，在准无许可且部分同步环境中，假设拜占庭参与者的总规模有界，存在一种确定性协议，保证在有限时间内解决拜占庭协议问题。（4）在准无许可且同步环境中，任何不使用高级密码学的权益证明协议都容易受到长程攻击。