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backward-reduction.tex

+49-18
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@@ -18,16 +18,21 @@ \subsection{Supersafety $\rightarrow$ Perfect Timeliness}\label{sec:backward-red
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\import{./}{algorithms/algorithm-backward-reduction.tex}
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\begin{figure}
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\begin{figure*}
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\centering
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\includegraphics[width=0.9\columnwidth,keepaspectratio]{figures/backward-reduction.pdf}
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\iflncs
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\includegraphics[width=0.9\columnwidth,keepaspectratio]{figures/backward-reduction.pdf}
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\fi
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\ifccs
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\includegraphics[width=1.4\columnwidth,keepaspectratio]{figures/backward-reduction.pdf}
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\fi
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\caption{The reduction from Supersafety
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(the $\Pi$ protocol) to Perfect Timeliness (the $\Pi^*$ protocol).
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New transactions of $\Ledger[][][r]$ are included in
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$\Ledger[*][][r]$ with recorded round $r$.
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}
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\label{fig:backward-reduction}
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\end{figure}
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\end{figure*}
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%We now prove that protocol $\Pi^*$ is perfectly timely.
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@@ -83,6 +88,29 @@ \subsection{A Perfectly Timely, Supersafe Protocol with Clients}
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Otherwise, the transaction is rejected as invalid.
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The protocol is illustrated in Figure~\ref{fig:client-support}.
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\ifccs
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\begin{figure*}[b]
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\centering
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\includegraphics[width=1\columnwidth,keepaspectratio]{figures/perfectly-timely-clients.pdf}
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\caption{Client support for the perfectly timely and supersafe protocol $\Pi*$.
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}
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\label{fig:client-support}
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\end{figure*}
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\fi
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\ifccs
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\begin{figure*}[b]
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\centering
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\includegraphics[width=0.75\columnwidth,keepaspectratio]{figures/perfectly-timely-clients-feedback.pdf}
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\caption{The client-supporting supersafe and perfectly timely protocol $\Pi^*$
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using only one instance of $\Pi$ for efficiency.
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Normal transactions and ledgers are shown in solid black lines;
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auxiliary transactions are shown in dashed
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orange lines.}
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\label{fig:client-support-feedback}
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\end{figure*}
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\fi
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A late-joining client first synchronizes $\Pi_1$ and $\Pi_2$ with the rest
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of the peers.
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Due to safety, liveness and the validity rule of $\Pi_2$,
@@ -94,13 +122,15 @@ \subsection{A Perfectly Timely, Supersafe Protocol with Clients}
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operating as a full online node without $\Pi_2$, i.e., it outputs the ledger $\Ledger[*]$.
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From this point on, the client is perfectly timely and supersafe.
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\begin{figure}
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\centering
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\includegraphics[width=0.7\columnwidth,keepaspectratio]{figures/perfectly-timely-clients.pdf}
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\caption{Client support for the perfectly timely and supersafe protocol $\Pi*$.
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}
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\label{fig:client-support}
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\end{figure}
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\iflncs
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\begin{figure*}
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\centering
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\includegraphics[width=0.7\columnwidth,keepaspectratio]{figures/perfectly-timely-clients.pdf}
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\caption{Client support for the perfectly timely and supersafe protocol $\Pi*$.
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}
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\label{fig:client-support}
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\end{figure*}
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\fi
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Lastly, to make this protocol efficient, we observe that the payload of
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$\Pi_2$ transactions does not need to include the whole $\Pi_1$ transaction, but
@@ -116,14 +146,15 @@ \subsection{A Perfectly Timely, Supersafe Protocol with Clients}
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only apply to the orange transactions. This final construction is illustrated in
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Figure~\ref{fig:client-support-feedback}.
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\begin{figure}
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\iflncs
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\begin{figure*}
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\centering
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\includegraphics[width=0.55\columnwidth,keepaspectratio]{figures/perfectly-timely-clients-feedback.pdf}
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\caption{The client-supporting supersafe and perfectly timely protocol $\Pi^*$
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using only one instance of $\Pi$ for efficiency.
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Normal transactions and ledgers are shown in solid black lines;
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auxiliary transactions are shown in dashed
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orange lines.}
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\label{fig:client-support-feedback}
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\end{figure}
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using only one instance of $\Pi$ for efficiency.
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Normal transactions and ledgers are shown in solid black lines;
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auxiliary transactions are shown in dashed
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orange lines.}
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\label{fig:client-support-feedback}
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\end{figure*}
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\fi

body.tex

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@@ -18,4 +18,6 @@
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\import{./}{forward-reduction.tex}
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\import{./}{backward-reduction.tex}
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\import{./}{conclusion.tex}
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\import{./}{acknowledgements.tex}
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\ifanonymous
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\import{./}{acknowledgements.tex}
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\fi

ccs-preamble.tex

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\fancyhf{} % Remove fancy page headers
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\fancyhead[C]{SBC '24} % TODO: replace 9999 with your paper number
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\fancyfoot[C]{\thepage}
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\acmConference[SBC]{SBC}{Aug 7 - 9, 2024}{Alfred Lerner Hall, Columbia University}
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\acmYear{}
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\acmPrice{}
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\acmDOI{}
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\acmISBN{}
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\fancypagestyle{firstpage}{
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\fancyhf{}
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\renewcommand{\footrulewidth}{0pt}
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\fancyfoot[C]{\vspace*{-3.5\baselineskip}\thepage}
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}
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\settopmatter{printacmref=false, printccs=false, printfolios=false}
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\setcopyright{none}
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\renewcommand\footnotetextcopyrightpermission[1]{}
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%%\ccsPaper{9999} % TODO: replace with your paper number once obtained

chains-to-ledgers.tex

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@@ -32,6 +32,15 @@ \subsection{From Chains to Ledgers}
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Furthermore, $\Chain[][P_1][r_1] \preccurlyeq \Chain[][P_1][r_2]$ (sticky).
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\end{definition}
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\ifccs
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\begin{figure*}
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\centering
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\includegraphics[width=0.7\columnwidth,keepaspectratio]{figures/freshness-timeliness.pdf}
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\caption{The chain in the proof of Theorem~\ref{thm:freshness-to-timeliness}.}
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\label{fig:freshness-to-timeliness}
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\end{figure*}
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\fi
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\noindent
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\textbf{From Temporal Blockchains to Temporal Ledgers.}
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Any temporal blockchain protocol can be transformed into a
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Because of freshness, it holds that $r_1 - r^* \leq w$.
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Therefore, from $r \leq r_1 - v$ it follows that $r - r^* \leq w - v = 0$.
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\begin{figure}
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\centering
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\includegraphics[width=0.5\columnwidth,keepaspectratio]{figures/freshness-timeliness.pdf}
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\caption{The chain in the proof of Theorem~\ref{thm:freshness-to-timeliness}.}
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\label{fig:freshness-to-timeliness}
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\end{figure}
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\iflncs
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\begin{figure*}
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\centering
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\includegraphics[width=0.5\columnwidth,keepaspectratio]{figures/freshness-timeliness.pdf}
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\caption{The chain in the proof of Theorem~\ref{thm:freshness-to-timeliness}.}
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\label{fig:freshness-to-timeliness}
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\end{figure*}
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\fi
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This is a contradiction because block $B$ extends a chain that contains $B^*$,
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and hence $r > r^*$.

forward-reduction.tex

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@@ -16,15 +16,20 @@ \subsection{Timeliness $\rightarrow$ Supersafety}
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The reduction is illustrated
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in Figure~\ref{fig:reduction-timeliness-supersafety} and Algorithm~\ref{alg:reduction-timeliness-supersafety}.
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\begin{figure}
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\begin{figure*}
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\centering
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\includegraphics[width=0.7\columnwidth,keepaspectratio]{figures/forward-reduction.pdf}
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\iflncs
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\includegraphics[width=0.7\columnwidth,keepaspectratio]{figures/forward-reduction.pdf}
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\fi
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\ifccs
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\includegraphics[width=1.1\columnwidth,keepaspectratio]{figures/forward-reduction.pdf}
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\fi
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\caption{The reduction from Timeliness
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(the $\Pi$ protocol) to Supersafety (the $\Pi^*$ protocol). A transaction is illustrated
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as a black circle and its recorded round is displayed below.
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}
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\label{fig:reduction-timeliness-supersafety}
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\end{figure}
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\end{figure*}
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When the \rread function is invoked, the temporal ledger of party $P$ is acquired
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in Line~\ref{line.reduction-t-s-ledger}.

frontpage.tex

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\import{./}{title.tex}
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\iflncs
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\maketitle
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\fi
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\iftoday
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\noindent
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\fi
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\import{./}{abstract.tex}
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\ifccs
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\maketitle
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\fi

introduction.tex

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the two properties are morally equivalent.
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\end{enumerate}
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\begin{figure}
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\begin{figure*}
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\centering
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% \includegraphics[width=1.0\columnwidth,keepaspectratio]{figures/timeliness-overview.pdf}
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\definecolor{myblue}{HTML}{cfe2f3}
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\draw[arrow] (braceMid) + (0,-5pt) -- (braceMid |- recency.north) node [pos=0.5, left, font=\footnotesize] {Lem~\ref{lem.longest-chain-recency}};
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\draw[arrow] (streamlet.east) -- (recency.west) node [pos=0.5, above, font=\footnotesize] {Thm~\ref{thm.streamlet-recency}};
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\coordinate (recencyMid) at ($(recency.south west)+(1.2cm,0)$);
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\draw[arrow] (recencyMid) -- (recencyMid |- freshness.north) node [left, pos=0.5, font=\footnotesize] {Thm~\ref{thm.recency-to-freshness}};
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and vice versa (Theorems~\ref{thm:timeliness-to-supersafety}-\ref{thm:backward-reduction}, bottom).
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}
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\label{fig:overview}
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\end{figure}
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\end{figure*}
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\noindent
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\textbf{Overview of the results.}

longest-chain-proof.tex

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For the second inequality, refer to Figure~\ref{fig:longest-chain-recency-proof}.
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\begin{figure}
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\begin{figure*}
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\centering
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\includegraphics[width=0.5\columnwidth,keepaspectratio]{figures/longest-chain-proof.pdf}
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\iflncs
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\includegraphics[width=0.5\columnwidth,keepaspectratio]{figures/longest-chain-proof.pdf}
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\fi
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\ifccs
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\includegraphics[width=0.8\columnwidth,keepaspectratio]{figures/longest-chain-proof.pdf}
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\fi
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\caption{Longest chain recency proof. Block $B'$ is illustrated in the
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earliest possible position.
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}
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\label{fig:longest-chain-recency-proof}
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\end{figure}
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\end{figure*}
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On the other hand, by Inequality~\ref{eq:bitcoin-r-bound}, $r - (r' + 2) \geq w - 1 \geq s$ and
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we can apply Chain Growth between rounds $r' + 2$ and $r$

preamble.sty

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\iflncs
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\usepackage{cite}
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\usepackage{amssymb}
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\fi
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% \usepackage{algorithmic}
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\usepackage{graphicx}
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\usepackage{textcomp}
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\usepackage{xspace}
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\usepackage[table,xcdraw,dvipsnames]{xcolor}
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%\usepackage[table,xcdraw,dvipsnames]{xcolor}
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\usepackage{tikz}
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\usepackage{mdframed}
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% \let\proof\relax
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% \let\endproof\relax
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{mathtools}
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\usepackage{xargs}
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\iflncs
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\usepackage{amssymb}
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\fi
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\iftwocolumn
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\usepackage{amsthm}
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\fi
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\PassOptionsToPackage{hyphens}{url}\usepackage{hyperref}
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\usepackage{bookmark}
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\usepackage{hyperref}
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\usepackage{mathtools}
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\usepackage{listings}
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\usepackage{import}
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\usepackage{algorithm}
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%pagestyle{plain}
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\ifccs
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% \iftwocolumn
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% \newtheorem{theorem}{Theorem}[section]
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% \newtheorem{corollary}{Corollary}[theorem]
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\newtheorem{lemma}[theorem]{Lemma}
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%
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\theoremstyle{remark}
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\newtheorem*{remark}{Remark}
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\newtheorem*{theorem*}{Theorem}
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%
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\theoremstyle{definition}
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\newtheorem{definition}{Definition}[section]
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% \fi
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\fi
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\iflncs
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\newtheorem{Lemma}{lemma}{lemma}
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\newenvironment{Claim}{claim}{claim}
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\newenvironment{Definition}{definition}{definition}
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\fi
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\ifccs

timeliness.tex

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%\anonymoustrue
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%\notestrue
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\lncstrue
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\todaytrue
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%\lncstrue
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\ccstrue
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%\todaytrue
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\ifccs
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\twocolumntrue

title.tex

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\title{On-Chain Timestamps Are Accurate}
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\ifanonymous{
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\author{}\institute{}
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}
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\ifanonymous{\iflncs
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\author{}\institute{}
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\fi}
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\else
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\author{
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Apostolos Tzinas\inst{2,3} \and
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Srivatsan Sridhar \inst{1} \and
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Dionysis Zindros\inst{1,3}
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}
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\iflncs
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\institute{
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Stanford University \and
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National Technical University of Athens \and
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Common Prefix
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}
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\else
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\affiliation{
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\institution{
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Stanford University \and
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National Technical University of Athens \and
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Common Prefix
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}
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}
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\fi
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\fi

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