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It's often said that State Machine Replication and Byzantine broadcast are equivalent (e.g., the abstract of [1]), but it seems only obvious how to reduce SMR to BB. I.e., give BB one can construct an SMR by rotating the leader.
What does it even mean to reduce BB to SMR then? In SMR, there are clients and servers, but in BB there are only servers.
[1] https://drops.dagstuhl.de/opus/volltexte/2018/9796/pdf/LIPIcs-DISC-2018-7.pdf
It means that, given an implementation of SMR, you can implement BB. For this, have each node in BB play both the role of an SMR server and the role of an SMR client. Then use the client interface to emulate broadcasting and delivering messages.
