Let L be a regular language, and define its verlan to be the language

u $($L$)=\{$uv$$u$,$v in $\backslash$Sigma $$ and vu in L$\}.$ In other words, a word w is in the verlan of L $,$ if it can be split into two words w$=$uv such that the swap vu of these two words is in L $.$ Provide a $2-$state DFA for L$=\{$a$\}^\{$b$\}^,$ the set of words of the form aa$$abb$$b $.$ Name the states of that DFA p and q $.$ A word w is in the verlan of L if either: $($Case p $)$ w can be written as uv $,$ with u being read from p to an accept state and v being read from the initial state to p $,$ or $($Case q $)$ w can be written as uv $,$ with u being read from q to an accept state and v being read from the initial state to p $.$ Provide an NFA for the verlan of L $.$ Each of the two cases above can be written using two copies of your DFA. For case p $,$ for instance, in the first copy, set p to be initial, and add $\backslash$epsi $-$transitions from any accept state to the initial state of the second copy. Then set p to be accepting in the second copy. To merge the two cases, simply use $\backslash$epsi $-$transitions as seen in class when we did the union with NFAs. Generalize the previous argument: Show that for any regular language, its verlan is regular. To do this, consider any DFA M$=($Q$,\backslash$Sigma $,\backslash$delta $,$q$0,$F$),$ and build NFAs for each of the cases. You can assume that the union of NFA languages is regular.