This paper revisits the ubiquitous problem of achieving state machine replication in blockchains based on repeated consensus, like Tendermint. To achieve state machine replication in blockchains built on top of consensus, one needs to guarantee fairness of user transactions. A huge body of work has been carried out on the relation between state machine replication and consensus in the past years, in a variety of system models and with respect to varied problem specifications. We systematize this work by proposing novel and rigorous abstractions for state machine replication and repeated consensus in a system model that accounts for realistic blockchains in which blocks may contain several transactions issued by one or more users, and where validity and order of transactions within a block is determined by an external application-dependent function that can capture various approaches for order-fairness in the literature. Based on these abstractions, we propose a reduction from state machine replication to repeated consensus, such that user fairness is achieved using the consensus module as a black box. This approach allows to achieve fairness as an add-on on top of preexisting consensus modules in blockchains based on repeated consensus.
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