Identify the language given by $L = \{ x \in (0,1)^* : x \neq ww^R, w \in (0,1)^*\}$. Note: $w^R$ is the reverse of the string $w$.Closure property can/should be applied only in the cases when the actual language is not specified. Otherwise, you may arrive at wrong conclusions. The language in question is fully specified, so I doubt whether one can directly apply closure property on $ww^R$, which you say, is its complement or vice versa. The given answer is CFL. But I don't seem to have arrived at it satisfactorily.
Is the complement of $ww^R$ context-free?
formal languages;context free