X-Git-Url: https://git.siccegge.de//index.cgi?p=talk%2Fcoalgebraic-mu-calculus-cool-2.git;a=blobdiff_plain;f=chapters%2Foptimizations.tex;h=9de0c1ee21368ba55319081a566077f97144f3ed;hp=6517e640778e5cceda51468cadfae5a4622d7c65;hb=HEAD;hpb=c23d4f4bb88ea0a9799ea81f40b780201ada016f

diff --git a/chapters/optimizations.tex b/chapters/optimizations.tex
index 6517e64..9de0c1e 100644
--- a/chapters/optimizations.tex
+++ b/chapters/optimizations.tex
@@ -1,17 +1,16 @@
 \section{Optimizing}
 \subsection*{Dummy}
 
-\begin{frame}{Semnatic Branching}
+\begin{frame}{Semantic Branching}
   \begin{itemize}
-  \item Idea: Add aditional information when considering second
-    alternative of an or: ${\phi \vee \psi}$ becomes ${\phi \vee
-      (¬\phi \wedge \psi)}$
-  \item Do not reexplore branches already known to be unsat already
+  \item Idea: Add additional information when considering second
+    alternative of a disjunction: ${\phi \vee \psi}$ becomes ${\phi
+      \vee (¬\phi \wedge \psi)}$
+  \item Do not re-explore branches already known to be unsatisfiable already
   \end{itemize}
 \end{frame}
 
 \begin{frame}{Non-atomic Negations}
-  TODO: ?
   \begin{itemize}
   \item Consider $\heartsuit\heartsuit\heartsuit{}p \wedge \overline{\heartsuit}\overline{\heartsuit}\overline{\heartsuit}¬p$
   \item Same as $\heartsuit\heartsuit\heartsuit{}p \wedge
@@ -40,11 +39,10 @@
   \end{itemize}
 \end{frame}
 
-
 \begin{frame}{Removing Edges}
   \begin{block}{Propagation}
     \begin{itemize}
-    \item Runs in $O(edge\cdot nodes)$
+    \item Runs in $\mathcal{O}(\mathit{|edge|}\cdot\mathit{|nodes|})$
     \item Needs to consider all satisfiable nodes
     \item Iterates over all edges
     \end{itemize}