Proof-of-stake blockchains require consensus protocols that support Dynamic Availability and Reconfiguration (which we call the DAR model). Here, Dynamic Availability means that the consensus protocol should remain live even if a large number of nodes temporarily crash, and Reconfiguration means it should be possible to change the set of operating nodes over time. State-of-the-art protocols inspired by the DAR model, such as Ethereum, Cardano's Ouroboros, or Snow White, require additional model features comprising external mechanisms or node capabilities that are difficult to justify, such as social consensus or the requirement that key evolution be performed even when nodes have crashed. The key result of this paper is the necessary and sufficient adversarial condition under which consensus can be achieved in the plain DAR model, without any extra features. We then introduce an additional feature to the model that is justified by proof-of-stake blockchain designs: honest nodes complete a sign-off procedure the moment they express intent to exit from the set of operating nodes. This additional feature reduces the power of the adversary relative to the plain DAR model and helps us obtain a bootstrapping gadget that is particularly simple and efficient in the common optimistic case of few reconfigurations and no double spending.

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