From Permissioned to Proof-of-Stake Consensus
Jovan Komatovic, Andrew Lewis-Pye, Joachim Neu, Tim Roughgarden, Ertem Nusret Tas

TL;DR
This paper introduces a universal compiler that converts permissioned consensus protocols into proof-of-stake permissionless protocols, preserving key properties and accountability in the process.
Contribution
It provides the first generic transformation method for converting permissioned protocols into proof-of-stake permissionless ones while maintaining essential properties.
Findings
Preserves consistency, liveness, and responsiveness in the transformed protocols.
Ensures accountability in the proof-of-stake protocols.
Maintains message complexity and composable properties.
Abstract
This paper presents the first generic compiler that transforms any permissioned consensus protocol into a proof-of-stake permissionless consensus protocol. For each of the following properties, if the initial permissioned protocol satisfies that property in the partially synchronous setting, the consequent proof-of-stake protocol also satisfies that property in the partially synchronous and quasi-permissionless setting (with the same fault-tolerance): consistency; liveness; optimistic responsiveness; every composable log-specific property; and message complexity of a given order. Moreover, our transformation ensures that the output protocol satisfies accountability (identifying culprits in the event of a consistency violation), whether or not the original permissioned protocol satisfied it.
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