MODULE $3$

Find the Regular Expression corresponding to the given automata.

Let $r1,r2$ be regular expression. Prove that there exists a $-$NFA for the following

cases and explain the construction procedure.

a$.r1+r2$

b$.$ r$1.$r$2$

c$.r1\{N\}\{$ Hint: $\{N\}$ indicates that $r1$ is matched exactly $N$ times $\}$

d$.r1?\{$ Hint: $r1$ is matched at most once $\}$

Show that the language is not a regular. Justify.

a$)L=\{\begin{array}{c}{0}^n|n\end{array}$ is a perfect square