Consider the argument that the language associated with any generalized transition graph is regular. The language associated with such a graph is
$L=\bigcup_{p∈P} L(r_p)$,
where $P$ is the set of all walks through the graph and $r_p$ is the expression associated with a walk $p$. The set of walks is generally infinite, so that in light of Exercise 21, it does not immediately follow that $L$ is regular. Show that in this case, because of the special nature of $P$, the infinite union is regular.
