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 difficult 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 model for reasoning about the rich design space of blockchain protocols and their capabilities and limitations in the permissionless setting. Our results demonstrate senses in which the permissionless setting is provably more challenging than its permissioned counterpart, and identify unavoidable protocol ingredients and additional assumptions that are necessary to achieve various forms of consensus in the permissionless setting.

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