More minor edits to pseudocode

diff --git a/doc/iotcloud.tex b/doc/iotcloud.tex
index f92126a2b96d543e7c14802003c91915648ea86f..e08d6e1d6826cc8c6c7a05cc38eac9f29e5f717e 100644 (file)
--- a/doc/iotcloud.tex
+++ b/doc/iotcloud.tex
@@ -587,7 +587,7 @@ $\tuple{ck,\tuple{k, v}} \in KV_s \wedge
 \r
 \begin{algorithmic}[1]\r
 \Function{Put}{$KV_s,\tuple{k_s,v_s}$}  \Comment{Interface function to update a key-value pair}\r
 \r
 \begin{algorithmic}[1]\r
 \Function{Put}{$KV_s,\tuple{k_s,v_s}$}  \Comment{Interface function to update a key-value pair}\r

-\State $\tuple{ck_s,\tuple{k_s,v_t}} \gets GetKVPair(KV,k_s)$\r
+\State $\tuple{ck_s,\tuple{k_s,v_t}} \gets GetKVPair(KV_s,k_s)$\r

 \If{$\tuple{ck_s,\tuple{k_s,v_t}} = \emptyset$}\r
        \State $KV_s \gets KV_s \cup \{\tuple{ck_p, \tuple{k_s,v_s}}\}$\r
        \State $ck_p \gets ck_p + 1$\r
 \If{$\tuple{ck_s,\tuple{k_s,v_t}} = \emptyset$}\r
        \State $KV_s \gets KV_s \cup \{\tuple{ck_p, \tuple{k_s,v_s}}\}$\r
        \State $ck_p \gets ck_p + 1$\r


@@ -951,9 +951,10 @@ call them $\mathsf{t}$ and $\mathsf{u}$ such that $\mathsf{s_t \le s_u}$.
 Then $\mathsf{t}$ is in the path of $\mathsf{u}$. \r
 \end{lem}\r
 \begin{proof}\r
 Then $\mathsf{t}$ is in the path of $\mathsf{u}$. \r
 \end{lem}\r
 \begin{proof}\r

-Assume otherwise. Then there are some pairs $\mathsf{(t,u)}$ that violate this lemma. \r
-Take a specific $\mathsf{(t,u)}$ such that $\mathsf{s_u}$ is minimized and \r
-$\mathsf{s_t}$ is maximized for this choice of $\mathsf{s_u}$.\r
+Assume that there are some pairs of messages $\mathsf{(t,u)}$ that violate this lemma. \r
+Take a specific $\mathsf{(t,u)}$ such that $\mathsf{s_u}$ is minimized, and \r
+$\mathsf{s_t}$ is maximized for this choice of $\mathsf{s_u}$. We will show that $\mathsf{C}$\r
+cannot receive both $\mathsf{t}$ and $\mathsf{u}$ without throwing an error.\r

 \r
 Clearly $\mathsf{C}$ will throw an error if $\mathsf{s_t = s_u}$. So \r
 $\mathsf{s_t < s_u}$. Additionally, if $\mathsf{C}$ receives $\mathsf{u}$ before \r
 \r
 Clearly $\mathsf{C}$ will throw an error if $\mathsf{s_t = s_u}$. So \r
 $\mathsf{s_t < s_u}$. Additionally, if $\mathsf{C}$ receives $\mathsf{u}$ before \r