update

[tt1516.git] / mbt_exercises / mbt.tex

diff --git a/mbt_exercises/mbt.tex b/mbt_exercises/mbt.tex
index 8efa296..064676e 100644 (file)
--- a/mbt_exercises/mbt.tex
+++ b/mbt_exercises/mbt.tex
@@ -1,7 +1,10 @@
 %&mbt
 \begin{document}
 
+% 1
 \section{Theory of Labelled Transition Systems}
+
+% 1.1
 \subsection{Testing equivalences}
 \begin{enumerate}[a)]
        \item $\bordermatrix{
@@ -65,6 +68,7 @@
                }$
 \end{enumerate}
 
+% 1.2
 \subsection{Testing equivalences}
 \begin{enumerate}[a)]
        \item $\bordermatrix{
@@ -132,6 +136,7 @@
                }$
 \end{enumerate}
 
+% 1.3
 \subsection{Testing equivalences}
 \begin{enumerate}[a)]
        \item
@@ -166,7 +171,26 @@
                \end{align*}
 \end{enumerate}
 
+% 1.4
 \subsection{Testing equivalences}
+\begin{enumerate}[a)]
+       \item $Q:=\xymatrix@C=1pc@R=1pc{
+                       \ar[dr]\\
+                       & *+[o][F-]{s_0}\ar@/_/[d]_a\\
+                       & *+[o][F-]{s_1}\ar@/_/[u]_b\ar@/_/[d]_a\\
+                       & *+[o][F-]{s_2}\ar@/_/[d]_a\ar@/_/[u]_b\\
+                       & \ldots\ar@/_/[u]_b\\
+               }$
+               $P:=\xymatrix@C=1pc@R=1pc{
+                       \ar[dr]\\
+                       & *+[o][F-]{s_0}\ar@/_/[d]_a\ar[r]^\tau & *+[o][F-]{s_0}\ar@(r,u)[]_b\\
+                       & *+[o][F-]{s_1}\ar@/_/[u]_b\ar@/_/[d]_a\ar@/_/[ur]_\tau\\
+                       & *+[o][F-]{s_2}\ar@/_/[d]_a\ar@/_/[u]_b\ar@/_1pc/[uur]_\tau\\
+                       & \ldots\ar@/_/[u]_b\ar@/_2pc/[uuur]_\tau\\
+               } $
+\end{enumerate}
+
+% 1.5
 \subsection{Testing equivalences}
 
 \end{document}