$(5$ points$)$:

aL$=\{0^($n$)10^($n$)$:n$>=0\}$ is

not regular.

$(5$ points$)$: Draw up a Push$-$down automaton which accepts the language

L$=\{$a$^($n$)$ba$^(2$n$)$:n$>=0\}.$

$($Cheggs system is breaking with images so please refer to the image to solve the problems at hand$)$