first.tex

   1 \subsection*{1.a}
   2 \emph{Consider the train gate controller example of slide 9, lecture
   3 \emph{Timed Automata}. Give an example of a series of timed transitions
   4 (including intermediate states) of the composed system (so the product
   5 construction of the three automata) showing a train approaching and finally
   6 leaving the gate.}
   7 \includegraphics[width=\linewidth]{1a}
   8
   9 \subsection*{1.b}
  10 \emph{Consider the timed automaton in figure 1 of the paper ”Timed Automata” by
  11 Rajeev Alur. Suppose initially we have a zone $(s0, [0 \leq x \leq 4, 0 \leq y
  12 \leq 3])$. Give the zone after a sequence a.b and show the intermediate steps
  13 in the derivation.}
  14
  15 \subsection*{1.c}
  16 \emph{Consider the timed automaton in figure 1 of the paper \emph{Timed
  17 Automata} by Rajeev Alur. Give the zone automaton of the timed automaton, with
  18 initial state $(s0, [x = 0, y = 0])$.}