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Merge pull request #45 from jamesray1/patch-8 

Moved footnote to body text on consensus safe decisions for readability
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Vlad Zamfir 2017-11-17 04:18:15 -04:00 committed by GitHub
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papers/CasperTFG/CasperTFG.tex
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@ -105,7 +105,7 @@ The proof refers to an ``estimator,'' which maps protocol states to propositions
An estimate in the binary consensus ($0$ or $1$) is said to be ``safe'' (have ``estimate safety'') for a particular protocol state if it is returned by the estimator on all future protocol states\footnote{I.e.\ all states accessible from that state through any valid protocol execution.}. In the blockchain consensus, a block is said to be ``safe'' for a particular protocol state if it is also in the fork choice for all future protocol states.
The consensus safety proof shows that decisions on safe estimates have consensus safety\footnote{Consensus safe decisions have the following property: any decisions made on safe estimates by a protocol following node will be \emph{consistent} with decisions made on safe estimates by any other protocol following node.} (as long as there are not more than $t$ Byzantine faults).
The consensus safety proof shows that decisions on safe estimates have consensus safety (as long as there are not more than $t$ Byzantine faults). Consensus safe decisions have the following property: any decisions made on safe estimates by a protocol following node will be \emph{consistent} with decisions made on safe estimates by any other protocol following node.
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}.