Define an FSA that accepts a string if and only if all the vowels within a

$--$ morpheme are identical. We will work with a very simple alphabet with one

$--$ consonant $`\text{'}$k$\text{'}`,$ two vowels $`\text{'}$i$\text{'}`$ and $`\text{'}$u$\text{'}`,$ and a space character for

$--$ morpheme boundaries $`\text{'}\text{'}`.$ Thus, for example, $`"$ikik kukku"$`,`"$kkuuk$"`,$ and

$--`"$ k i u$"`$ should all be accepted, but $`"$kiku$"`$ should not be$.$