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This paper revisits the ubiquitous problem of achieving state machinereplication in blockchains based on repeated consensus, like Tendermint. Toachieve state machine replication in blockchains built on top of consensus, oneneeds to guarantee fairness of user transactions. A huge body of work has beencarried out on the relation between state machine replication and consensus inthe past years, in a variety of system models and with respect to variedproblem specifications. We systematize this work by proposing novel andrigorous abstractions for state machine replication and repeated consensus in asystem model that accounts for realistic blockchains in which blocks maycontain several transactions issued by one or more users, and where validityand order of transactions within a block is determined by an externalapplication-dependent function that can capture various approaches fororder-fairness in the literature. Based on these abstractions, we propose areduction from state machine replication to repeated consensus, such that userfairness is achieved using the consensus module as a black box. This approachallows to achieve fairness as an add-on on top of preexisting consensus modulesin blockchains based on repeated consensus.

SoK: Achieving State Machine Replication in Blockchains based on Repeated Consensus