Let

$\backslash$Sigma $2=$

$0$

$0$

$,$

$0$

$1$

$,$

$1$

$0$

$,$

$1$

$1$

$.$

Consider the top and bottom rows to be strings of $0$s and $1$s$.$ For each of the following

languages, determine if they are regular $($or not$)$:

$($a$)$ L$4$a $=$

w in $\backslash$Sigma

$$

$2$

$|$ the bottom row of w is three times the top row

$($b$)$ L$4$b $=$

w in $\backslash$Sigma

$$

$2$

$|$ each row of w contains a equal number of $1$s