+(* It is now clear that we can build a DFA D_e for e by taking pre as states,
+and move as transition function; the initial state is •(e) and a state 〈i,b〉 is
+final if and only if b is true. The fact that states in D_e are finite is obvious:
+in fact, their cardinality is at most 2^{n+1} where n is the number of symbols in
+e. This is one of the advantages of pointed regular expressions w.r.t. derivatives,
+whose finite nature only holds after a suitable quotient.
+
+Let us discuss a couple of examples.
+Below is the DFA associated with the regular expression (ac+bc)*.
+
+\includegraphics[width=.8\textwidth]{acUbc.pdf}
+\caption{DFA for $(ac+bc)^*$\label{acUbc}}
+
+The graphical description of the automaton is the traditional one, with nodes for
+states and labelled arcs for transitions. Unreachable states are not shown.
+Final states are emphasized by a double circle: since a state 〈e,b〉 is final if and
+only if b is true, we may just label nodes with the item.
+The automaton is not minimal: it is easy to see that the two states corresponding to
+the items (a•c +bc)* and (ac+b•c)* are equivalent (a way to prove it is to observe
+that they define the same language!). In fact, an important property of pres e is that
+each state has a clear semantics, given in terms of the specification e and not of the
+behaviour of the automaton. As a consequence, the construction of the automaton is not
+only direct, but also extremely intuitive and locally verifiable.
+
+Let us consider a more complex case.
+Starting form the regular expression (a+ϵ)(b*a + b)b, we obtain the following automaton.
+
+\includegraphics[width=.8\textwidth]{automaton.pdf}
+\caption{DFA for $(a+\epsilon)(b^*a + b)b$\label{automaton}}
+
+Remarkably, this DFA is minimal, testifying the small number of states produced by our
+technique (the pair ofstates $6-8$ and $7-9$ differ for the fact that $6$ and $7$
+are final, while $8$ and $9$ are not).
+*)
+