.

diff --git a/e2.tex b/e2.tex
new file mode 100644 (file)
index 0000000..ad644cf
--- /dev/null
+++ b/e2.tex
@@ -0,0 +1,64 @@
+\documentclass{article}
+
+\usepackage{a4wide}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage[all]{xypic}
+
+\newcommand{\ra}{\rightarrow}
+\newcommand{\un}{\text{ \textsf{U} }}
+\newcommand{\ev}{\lozenge}
+\newcommand{\al}{\square}
+\newcommand{\nx}{\bigcirc}
+
+\everymath{\displaystyle}
+
+\begin{document}
+\begin{enumerate}
+       \item
+               $\xymatrix{
+                       & l_0 & l_1 & l_2 & l_3 & l_5 & l_6 & l_7\\
+                       l_0\\
+                       l_1\\
+                       l_2\\
+                       l_3\\
+                       l_5\\
+                       l_6\\
+                       l_7
+               }$
+       \item
+               $\al(crit_0\veebar crit_1)$
+       \item 
+               We define:\\
+               $ AP=\bigcup_{i\in N}\{lift_n, door_n,call_n\},
+               N=\{0, 1, 2, 3\}$
+               \begin{enumerate}
+                       \item
+                               $\bigwedge_{n\in N}\al(door_m\ra lift_n)$
+                       \item
+                               $\bigwedge_{n\in N}\al(call_n\ra\ev(lift_n\wedge door_n))$
+                       \item
+                               $\al\ev lift_0$
+                       \item
+                               $\al(call_3\rightarrow\bigcirc (lift_3\wedge door_3))$
+               \end{enumerate}
+       \item\strut\\
+               $\begin{array}{ll}
+                       \varphi_1=\ev\al c & 
+                               s_2\ra s_4\overline{\ra s_5}\\
+                       \varphi_2=\al\ev c &
+                               s_2\ra s_4\overline{\ra s_5}\\
+                       \varphi_3=\nx\neg c\rightarrow\nx\nx c &
+                               s_2\ra s_4\overline{\ra s_5}\\
+                       \varphi_4=\al a & 
+                               \text{Impossible. $a$ only holds in $s_1$ and in $s_5$.}\\
+                       & \text{$s_1$ we can only leave through a state where $\neg a$}\\
+                       & \text{$s_5$ we can not reach through $s_1$ without passing
+                               through a $\neg a$ state}\\
+                       \varphi_5=a\un\al(b\vee c) &
+                               s_1\ra s_4\overline{\ra s_5}\\
+                       \varphi_6=(\nx\nx b)\un(b\vee c) &
+                               s_2\ra s_4\overline{\ra s_5}
+               \end{array}$
+\end{enumerate}
+\end{document}