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Fix typo decribed -> described and return -> returned

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Kent Shikama 2018-01-15 00:17:59 +09:00
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papers/CasperTFG/CasperTFG.tex
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@ -361,7 +361,7 @@ We now have the language required to define the estimator for the blockchain con
\caption{The Greedy Heaviest-Observed Sub-tree Fork-choice rule, $\mathcal{E}$}
\end{algorithm}
We assume that ``hash'' has the property that out of any set of blocks, only one has the lowest hash. Using the hashes of blocks to eliminate ``ties'' means that the estimator for the blockchain consensus never outputs an exception. Previously the binary estimator return $\emptyset$ when $0$ and $1$ had the same score. This means that a message $m$ is valid if $E(m) = \mathcal{E}(J(m))$, and just as in the binary consensus we insist that all the blocks are valid. \footnote{Following the process decribed in the footnote about excluding invalid messages from the binary consensus.}
We assume that ``hash'' has the property that out of any set of blocks, only one has the lowest hash. Using the hashes of blocks to eliminate ``ties'' means that the estimator for the blockchain consensus never outputs an exception. Previously the binary estimator returned $\emptyset$ when $0$ and $1$ had the same score. This means that a message $m$ is valid if $E(m) = \mathcal{E}(J(m))$, and just as in the binary consensus we insist that all the blocks are valid. \footnote{Following the process described in the footnote about excluding invalid messages from the binary consensus.}
``Equivocation'', ``Byzantine faulty'', ``fault weight'', ``protocol states'', and ``protocol executions'' are defined here in \emph{precisely} the same way as in the binary consensus. We therefore do not give the definitions again.