LTL semantics.
1.1 --- a/slides/src/slides.tex Thu Jul 21 00:53:49 2011 +0200
1.2 +++ b/slides/src/slides.tex Thu Jul 21 01:41:30 2011 +0200
1.3 @@ -430,6 +430,45 @@
1.4 \end{frame}
1.5
1.6 \begin{frame}
1.7 +\frametitle{Linear Temporal Logic}
1.8 +\framesubtitle{Satisfiability}
1.9 +\begin{def:satisfiability}
1.10 +A model $\M = (\F, V)$ \emph{satisfies} a formula $\varphi$ at time instant $i$ is denoted by $\M,i \models \varphi$:
1.11 +\begin{itemize}
1.12 +\item $\M,i \models p$ for $p \in \Prop \iff p \in V(i)$
1.13 +\item $\M,i \models \neg \varphi \iff$ not $\M,i \models \varphi$
1.14 +\item $\M,i \models \varphi \lor \psi \iff \M,i \models \varphi$ or $\M,i \models \psi$
1.15 +\item $\M,i \models \X \varphi \iff \M,i+1 \models \varphi$
1.16 +\item $\M,i \models \varphi \U \psi \iff \exists{k \geq i}: \M,k \models \psi$ and $\forall{i \leq j < k}: \M,j \models\varphi$
1.17 +\end{itemize}
1.18 +\end{def:satisfiability}
1.19 +\end{frame}
1.20 +
1.21 +\begin{frame}
1.22 +\frametitle{Linear Temporal Logic}
1.23 +\framesubtitle{Model Example}
1.24 +\begin{figure}
1.25 +\centering
1.26 +\begin{tikzpicture}[shorten >=1pt, node distance=2.5cm, auto, semithick, >=stealth
1.27 + ,accepting/.style={fill, gray!50!black, text=white}]
1.28 +\node[state, initial, initial text=] (s_0) {$\{p_0\}$};
1.29 +\path (s_0) [late options={label=below:$s_0$}];
1.30 +\node[state] (s_1) [right of= s_0] {$\{p_0, p_2\}$};
1.31 +\path (s_1) [late options={label=below:$s_1$}];
1.32 +\node[state] (s_2) [right of= s_1] {$\{p_1\}$};
1.33 +\path (s_2) [late options={label=below:$s_2$}];
1.34 +\node[state] (s_i) [right of= s_2] {$\{p_1\}$};
1.35 +\path (s_i) [late options={label=below:$s_i$}];
1.36 +\path[->]
1.37 +(s_0) edge node {$R$} (s_1)
1.38 +(s_1) edge node {$R$} (s_2);
1.39 +\path[dashed,->]
1.40 +(s_2) edge node {$R$} (s_i);
1.41 +\end{tikzpicture}
1.42 +\end{figure}
1.43 +\end{frame}
1.44 +
1.45 +\begin{frame}
1.46 \frametitle{Model Checking}
1.47 \framesubtitle{A bit more information about this}
1.48