$($I$)$ State the pumping lemma with all its conditions and indicate how you go about

proving that a language is not regular.

$($II$)$ If the languages are regular, give an automaton. Otherwise, show it is not

regular by using pumping lemma.

$L=\{b^2{a}^n{b}^m{a}^3|m,n0\}$

$L=\{b^2{a}^n{b}^m{a}^3|m=n\}.$

$L=\{w{w}^R|wis$ any string over $\{a*b\}\}$

$L=\{a^3{b}^4\}$

$L=\{a^n{b}^{n+1}\}$

$L=\{a^m{b}^n{a}^{m+n}|m,n0\}$