This article explains how Practical Byzantine Fault Tolerance (PBFT) builds on Lamport’s theoretical consensus algorithms by introducing leaders, quorums, and cryptographic optimizations to make Byzantine consensus practical, contrasts it with Paxos and crash-fault tolerance, and explores its influence on modern blockchain protocols.

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This article, following Lamport's work, extends the original Byzantine Generals algorithm from “oral-messages” to signed messages, showing how digital signatures drastically simplify the problem and reduce message complexity, with an implementation given in Python using Flask HTTP nodes.

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This article examines where Lamport's original oral-messages Byzantine Generals algorithm does and does not apply in practice, contrasting unsuitable cases like distributed databases and rocket launches with a suitable case in redundant flight control systems.

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This follow-up factors Lamport’s Byzantine Generals algorithm into a generalized class that's independent of I/O and payloads. Any node can initiate a round (be "king"), values can be arbitrary strings, and multiple rounds can run concurrently.

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I discuss Lamport's Byzantine Generals problem and why it requires a total of N≥3M+1 nodes with M malicious nodes, and then implement the solution using Python with HTTP Flask servers.

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