On Finality in Blockchains

This paper focuses on blockchain finality, which refers to the time when it becomes impossible to remove a block that has previously been appended to the blockchain. Blockchain finality can be deterministic or probabilistic, immediate or eventual. To favor availability against consistency in the face of partitions, most blockchains only offer probabilistic eventual finality: blocks may be revoked after being appended to the blockchain, yet with decreasing probability as they sink deeper into the chain. Other blockchains favor consistency by leveraging the immediate finality of Consensus - a block appended is never revoked - at the cost of additional synchronization. The quest for "good" deterministic finality properties for blockchains is still in its infancy, though. Our motivation is to provide a thorough study of several possible deterministic finality properties and explore their solvability. This is achieved by introducing the notion of bounded revocation, which informally says that the number of blocks that can be revoked from the current blockchain is bounded. Based on the requirements we impose on this revocation number, we provide reductions between different forms of eventual finality, Consensus and Eventual Consensus. From these reductions, we show some related impossibility results in presence of Byzantine processes, and provide non-trivial results. In particular, we provide an algorithm that solves a weak form of eventual finality in an asynchronous system in presence of an unbounded number of Byzantine processes. We also provide an algorithm that solves eventual finality with a bounded revocation number in an eventually synchronous environment in presence of less than half of Byzantine processes. The simplicity of the arguments should better guide blockchain designs and link them to clear formal properties of finality.