Given a string w over an alphabet $\Sigma$ we define symmetric string the string $w^R$ defined as follows:
if $w=\epsilon$ ($\epsilon$ is empty string)
if $w=\sigma x$ with $\sigma\in\Sigma$ and $x\in\Sigma^*$, where $\Sigma^*$ is the set of all strings defined on the alphabet $\Sigma$ (including the empty string).
Then $w^R=x^R\sigma$.
Clearly $(w^R)^R=w$.
Example: if $w=road$ then $w^R=daor$.
In class, my professor gave to solve the following exercise.
Exercise: Define the grammar that generates the language $\{x|exist\ \ w \ \ such\ \ that\ \ x=ww^R\}$
Any suggestions please?
Thank you very much