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I have seen several blog articles (e.g here and here) mention about the BFT consensus integration effort to Tezos. They gave me an impression that the current consensus protocol in Proto003 has no BFT property.
What type of consensus algorithm is used now, and what kind of safety property of it is formally/informally proven or expected?
Tezos is going in the direction of BFT for two reasons:
Today, Proto_003 is still using the initial consensus algorithm, which has not yet been proven correct (and the work on BFT makes such effort useless in the short term as it will be replaced soon). The closest formally proven work to the current consensus algorithm is probably Ouroboros, but not yet implemented in Cardano.
