Else possibilities Clause Samples

Else possibilities. Because no honest node has ever seen 2tmax + 1 pre-commit messages, lockvalueq = for all honest node q. Thus, they will identify their leader by their local view. Because all honest nodes start at the r-th iteration within time λ, they can receive all the initial values from other honest nodes before identifying the leaders. Thus, there exist some honest nodes that pre-commit different values relative to each other only if a Byzantine node proposes different initial values to different nodes7. However, the honest nodes will propagate the initial value so all honest nodes will have the same set of initial values after time λ. Thus, to prevent the honest nodes from agreeing on the same leader, Byzantine nodes must propose different initial values to different nodes at every iteration. However, a node can only propose an initial value once, or it will be caught. Thus, the best strategy of Byzantine nodes is that different Byzantine nodes propose their initial values at different iterations so t Byzantine nodes can only interfere during t iterations. Thus, all the honest nodes will decide on some values in t + 1 iterations with certainty. ≤
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