# Is the Complement of the Language $L=\{wxw^r|w \in (a+b)^+, x \in (a+b) \}$ Context free?

Discussion in 'Computer Science' started by user3767495, Oct 8, 2018.

1. ### user3767495Guest

I know that the Context-free languages are not closed under compliment.

Given $L=\{wxw^r| w \in(a+b)^+,x \in (a+b)\}$ and this is a Context free language. I think it's compliment will contain words of the form $ww$ which comes under CSL.So, I think this $\lnot L$ must be not context-free.But I've read here

Why are palindrome and not-palindrome both context-free?

that palindromes are closed under complement.

Can someone please guide over this?