From e8fad69936e3903e8a4dbbd4d2ef5954539d23f2 Mon Sep 17 00:00:00 2001
From: rtrimana <rtrimana@uci.edu>
Date: Tue, 12 Jul 2016 10:56:12 -0700
Subject: [PATCH] Using \tuple{} for expressing tuples

---
 doc/iotcloud.tex | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/doc/iotcloud.tex b/doc/iotcloud.tex
index 7952545..f7c7ea1 100644
--- a/doc/iotcloud.tex
+++ b/doc/iotcloud.tex
@@ -134,12 +134,12 @@ $slot_s = \tuple{s, sv} \in SL \subseteq SN \times SV$ \\
 \textit{max = maximum number of slots (input only for resize message)} \\
 \textit{n = number of slots} \\ \\
 \textbf{Helper Function} \\
-$MaxSlot(SL')= \langle s, sv \rangle \mid \langle s, sv \rangle 
-\in SL' \wedge \forall \langle s', sv' \rangle \in SL', s \geq s'$ \\
-$MinSlot(SL')= \langle s, sv \rangle \mid \langle s, sv \rangle 
-\in SL' \wedge \forall \langle s', sv' \rangle \in SL', s \leq s'$ \\
-$SeqN(\langle s, sv \rangle)=s$ \\
-$SlotVal(\langle s, sv \rangle)=sv$ \\
+$MaxSlot(SL')= \tuple{s, sv} \mid \tuple{s, sv}
+\in SL' \wedge \forall \tuple{s', sv'} \in SL', s \geq s'$ \\
+$MinSlot(SL')= \tuple{s, sv} \mid \tuple{s, sv} 
+\in SL' \wedge \forall \tuple{s', sv'} \in SL', s \leq s'$ \\
+$SeqN(\tuple{s, sv})=s$ \\
+$SlotVal(\tuple{s, sv})=sv$ \\
 
 \begin{algorithmic}[1]
 \Function{GetSlot}{$s_g$}
@@ -152,19 +152,19 @@ $SlotVal(\langle s, sv \rangle)=sv$ \\
 \If{$(max' \neq \emptyset)$}\Comment{Resize}
 \State $max \gets max'$
 \EndIf
-\State $\langle s_n,sv_n \rangle \gets MaxSlot(SL)$\Comment{Last sv}
-\State $s_n \gets SeqN(\langle s_n,sv_n \rangle)$
+\State $\tuple{s_n,sv_n} \gets MaxSlot(SL)$\Comment{Last sv}
+\State $s_n \gets SeqN(\tuple{s_n,sv_n})$
 \If{$(s_p = s_n + 1)$}
 	\If{$n = max$}
-    	\State $\langle s_m,sv_m \rangle \gets MinSlot(SL)$\Comment{First sv}
-		\State $SL \gets SL - \{\langle s_m,sv_m \rangle\}$
+    	\State $\tuple{s_m,sv_m} \gets MinSlot(SL)$\Comment{First sv}
+		\State $SL \gets SL - \{\tuple{s_m,sv_m}\}$
 	\Else \Comment{$n < max$}
 		\State $n \gets n + 1$
 	\EndIf
-    \State $SL \gets SL \cup \{\langle s_p,sv_p \rangle\}$
+    \State $SL \gets SL \cup \{\tuple{s_p,sv_p}\}$
 	\State \Return{$true$}
 \Else
-	\State \Return{$(false,\{\langle s,sv \rangle \in SL \mid 
+	\State \Return{$(false,\{\tuple{s,sv}\in SL \mid 
     s \geq s_p\})$}
 \EndIf
 \EndFunction
-- 
2.34.1