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[talk/coalgebraic-mu-calculus-cool-2.git] / chapters / optimizations.tex

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+\section{Optimizing}
+\subsection*{Dummy}
+
+\begin{frame}{Semnatic 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
+  \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 $\heartsuit\heartsuit\heartsuit{}p \wedge
+    ¬\heartsuit\heartsuit\heartsuit{}p$ and thus obviously unsatisfiable
+  \item Cool normalizes formulas to make best use of Global Caching
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Subset Nodes}
+  \begin{itemize}
+  \item Lemma: If some Node is already satisfiable, all Nodes with
+    subsets of formulas, deferrals are also satisfiable
+  \item Too expensive to check in general\pause
+  \item Might be interesting for Nodes with full focus and its
+    siblings with the same set of formulas
+  \item Cheap but does this happen often?
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Normalization}
+  TODO: ?
+  \begin{itemize}
+  \item Global Caching better with more same formulas
+  \item Preprocessing in Cool currently does not consider
+    (propositional) Comutativity, Associativity or Distributivity laws
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Removing Edges}
+  \begin{block}{Propagation}
+    \begin{itemize}
+    \item Runs in $O(edge\cdot nodes)$
+    \item Needs to consider all satisfiable nodes
+    \item Iterates over all edges
+    \end{itemize}
+  \end{block}\pause
+  \begin{itemize}
+  \item Idea: Remove unneeded edges
+  \item Cores are $\exists$-quantified -- all unsatisfiable children
+    may be removed
+  \item States are essentially $\forall$-quantified -- all satisfiable
+    children may be removed
+  \end{itemize}
+\end{frame}
+
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "../vortrag"
+%%% TeX-engine: luatex
+%%% TeX-PDF-mode: t
+%%% End: