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Merge pull request #47 from jamesray1/patch-9 

have *a* common future
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Vlad Zamfir 2017-11-17 04:19:22 -04:00 committed by GitHub
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papers/CasperTFG/CasperTFG.tex
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@ -109,7 +109,7 @@ The consensus safety proof shows that decisions on safe estimates have consensus
The proof relies on the following key result: If node $1$ with state $\sigma_1$ has safe estimate $e_1$ and another node $2$ with state $\sigma_2$ has safe estimate $e_2$, \emph{and if they have a future state in common $\sigma_3$}, then node $1$ and node $2$'s decisions on $e_1$ and $e_2$ are consistent. The result is quite simple as it follows without much work from the definition of estimate safety. Specifically, if a state $\sigma$ has a safe estimate $e$, then any future protocol state of $\sigma$, $\sigma'$, is also safe on $e$. So if our states $\sigma_1$ and $\sigma_2$ (with safety on $e_1$ and $e_2$) share a common future, then that future has to be safe on both $e_1$ \emph{and} $e_2$, which means that they are consistent. So this first part of the proof shows that decisions on safe estimates are consensus safe \emph{for any pair of nodes who have a future protocol state in common}.
Next we aim to construct protocols (``protocol states'' with ``state transitions'') which guarantee that nodes have common future protocol states unless there are more than $t$ Byzantine faults. Such a protocol has consensus safety if there are not more than $t$ such faults, from the result we just discussed. We accomplish this in a few steps.
Next we aim to construct protocols (``protocol states'' with ``state transitions'') which guarantee that nodes have a common future protocol states unless there are more than $t$ Byzantine faults. Such a protocol has consensus safety if there are not more than $t$ such faults, from the result we just discussed. We accomplish this in a few steps.
First, we assume that protocol states are sets of protocol messages and then insist that the union $\sigma_1 \cup \sigma_2$ of any two protocol states $\sigma_1$ and $\sigma_2$ is itself a protocol state. Further, we insist that there is a state transition from each protocol state $\sigma$ to $\sigma' \supset \sigma$ (any superset of $\sigma$). This means that $\sigma_1 \cup \sigma_2$ is a protocol future of $\sigma_1$ and $\sigma_2$.