I encountered this problem involving manipulating a context-free language. Let $L$ be a context-free language. Define $L^{\#} = \{ x : x^i \in L$ for every $i=0,1,2,...\}$. Is $L^{\#}$ always context-free?My guess is that it will preserve context-freeness. Can anyone provide an elementary proof of this?
Does the following transformation preserve context-freeness?
formal languages;context free