\subsection*{1.a}
\emph{Consider the train gate controller example of slide 9, lecture
\emph{Timed Automata}. Give an example of a series of timed transitions
(including intermediate states) of the composed system (so the product
construction of the three automata) showing a train approaching and finally
leaving the gate.}
\begin{figure}[h]
	\centering
	\includegraphics[width=.3\linewidth]{1a}
	\caption{Timed transitions of the composed system}
\end{figure}

\subsection*{1.b}
\emph{Consider the timed automaton in figure 1 of the paper ”Timed Automata” by
Rajeev Alur. Suppose initially we have a zone $(s0, [0 \leq x \leq 4, 0 \leq y
\leq 3])$. Give the zone after a sequence a.b and show the intermediate steps
in the derivation.}

\subsection*{1.c}
\emph{Consider the timed automaton in figure 1 of the paper \emph{Timed
Automata} by Rajeev Alur. Give the zone automaton of the timed automaton, with
initial state $(s0, [x = 0, y = 0])$.}
