Problem $7$

Let COMPLETES$\_$R in $L,wx$ in $R,$ where $R$ is some regular language. In other words, it's

the language of all strings which when appended to the front of some string in L$,$ create a string in

R$.$

Prove by construction on PDAs that the set of context$-$free languages is closed under

COMPLETES$\_$R for all R$.$

Hint: think about what transitions we should be following when reading the input, and what to do

afterward