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Can I clarify my understanding:

Byzantine Fault Tolerance is a characteristic of a system to tolerate a class of failures belonging to the byzantine generals problem.

Byzantine Fault tolerance is also the name of the consensus algorithm that solves the byzantine generals problem?

I see Ripple as being BFT. Does it mean it uses some custom algorithm, that solves BFT?

I also see Stellar uses BFT, does this mean that Stellar and Ripple Both use different algorithms that solve BFT?

Edit:

Can all Proof of Insert word algorithms be seen to be a part of BFT? Because POW uses a probabilistic model to solve the generals problem, but it is not seen as BFT.

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To answer your question, no.

BFT-class consensus algorithms seek to solve the Byzantine Generals Problem.

Other consensus algorithms, generally the Nakamato-style consensus algorithms) including PoW (Proof-of-Work, used by Bitcoin) and PoET (Proof of Elapsed Time, used by Sawtooth) do not seek to solve BFT.

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There are quite a few confusions here. In a nutshell / on an extremely high level:

You are correct that BFT is a generally desirable characteristic of a system. Basically, it just means that people can't fraud the consensus system.

Since you're asking in bitcoin.stackexchange.com BFT is pretty much the main thing people are trying to get, without sacrificing too much of other properties. So yes, you can say that all "insert word algorithms" are trying to get BFT because that is basically the premise/foundation of any trustless distributed system.

The algorithm that Ripple/Stellar use are called / are based on an algorithm called PBFT (Practical Byzantine Fault Tolerance), which is an unfortunately confusing name.

Now since Stellar forked from Ripple it is no surprise that they happen to be using the same / similar consensus algorithm.

Different consensus algorithms take different "sacrifices" to "solve BFT". PoW sacrifices transaction throughput and energy to achieve BFT. PBFT sacrifices decentralization / censorship-resistance.

  • PoW does not solve BFT. It only probabilistically solves it, and only under certain economic assumptions. – Pieter Wuille Sep 7 '18 at 3:55

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