// qed.
(*
-Example. Let us consider the item
+\ 5b\ 6Example\ 5/b\ 6. Let us consider the item
(•a + ϵ)((•b)*•a + •b)b
whose finite nature only holds after a suitable quotient.
Let us discuss a couple of examples.
+
+\ 5b\ 6Example\ 5/b\ 6.
Below is the DFA associated with the regular expression (ac+bc)*.
-\includegraphics[width=.8\textwidth]{acUbc.pdf}
-\caption{DFA for $(ac+bc)^*$\label{acUbc}}
+\ 5img src="acUbc.gif" alt="some_text"/\ 6
The graphical description of the automaton is the traditional one, with nodes for
states and labelled arcs for transitions. Unreachable states are not shown.
only direct, but also extremely intuitive and locally verifiable.
Let us consider a more complex case.
+
+\ 5b\ 6Example\ 5/b\ 6.
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}}
+\ 5img src="automaton.pdf" alt="some_text"/\ 6
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 $7$