\subsection{Server Algorithm}\r
$s \in SN$ is a sequence number\\\r
$sv \in SV$ is a slot's value\\\r
-$slot_s = \tuple{s, sv} \in Q \subseteq SN \times SV$ \\\r
+$slot_s = \tuple{s, sv} \in SL \subseteq SN \times SV$ \\\r
\r
\textbf{State} \\\r
-\textit{Q = set of live slots on server} \\\r
+\textit{SL = set of live slots on server} \\\r
\textit{max = maximum number of slots (input only for resize message)} \\\r
\textit{n = number of slots} \\\r
\r
\begin{algorithmic}[1]\r
-\Function{Get}{$s'$}\r
-\State \Return{$\{\tuple{s, sv} \in Q \mid s \geq s'\}$}\r
+\Function{GetSlot}{$s_g$}\r
+\State \Return{$\{\tuple{s, sv} \in SL \mid s \geq s_g\}$}\r
\EndFunction\r
\end{algorithmic}\r
\r
\begin{algorithmic}[1]\r
-\Function{Put}{$s,newMax,newSlot$}\r
-\If{$(newMax \neq \emptyset) \land (newMax > max)$}\Comment{Resize}\r
- \State $Q' \gets \{slot_1, slot_2, \dots, slot_{newMax}\} \forall slot_i = 0 \r
- \Leftrightarrow Q' = \emptyset$\r
- \State $Q \gets Q' \cup Q$\r
- \State $max \gets newMax$\r
+\Function{PutSlot}{$s_p,sv_p,max'$}\r
+\If{$(max' \neq \emptyset)$}\Comment{Resize}\r
+\State $max \gets max'$\r
\EndIf\r
-\If{$(s = sn_n + d)$}\r
+\State $s_n \gets \{\langle s,sv \rangle \in SL \mid \r
+ \forall \langle s_i,sv_i \rangle \in SL, s \geq s_i\}$\Comment{Last s}\r
+\If{$(s_p = s_n + 1)$}\r
\If{$n = max$}\r
- \State $Q \gets Q - \{slot_{sn_1}\}$\r
- \State $SN \gets SN - \{sn_1\}$\r
- \State $Q \gets Q \cup newSlot$\r
+ \State $SL \gets SL - \{\langle s,sv \rangle \in SL \mid \r
+ \forall \langle s_i,sv_i \rangle \in SL, s \leq s_i\}$\Comment{First s}\r
\Else \Comment{$n < max$}\r
- \State $Q \gets Q \cup newSlot$\r
\State $n \gets n + 1$\r
\EndIf\r
- \State $SN \gets SN \cup \{s\: |\: s = new\: sn_n\}$\r
- \State $status \gets true$\r
- \State $MSlot \gets \emptyset$\r
+ \State $SL \gets SL \cup \{\langle s_p,sv_p \rangle\}$\r
+ \State \Return{$true$}\r
\Else\r
- \State $status \gets false$\r
- \State $MSlot \gets \{slot_{s}, \dots, slot_{sn_n}\} \forall $\r
- $slot_i = \langle i,E( \langle k,v \rangle ) \rangle \in Q$\r
+ \State \Return{$(false,\{\langle s,sv \rangle \in SL \mid \r
+ s \geq s_p\})$}\r
\EndIf\r
-\State \Return{$\langle status,MSlot \rangle$}\Comment{Return missed updates and status}\r
\EndFunction\r
\end{algorithmic}\r
\r