Finding a grammar for a formal language I am looking for a grammar that describes the formal language $L = \\{ xyx^R \;|\; x,y \in \\{a,b\\}^*\\}$ where $\\{a,b\\}^*$ corresponds to the regular expression _[ab]_ *. If there would be no y and the language would therefore contain all the words that are palindromes there wouldn't be any problem. I just don't get the "y" included therein. Could you please help me to find a solution? Thanks in advance

* S -> aSa | bSb | A
* A -> aA | bA | $\varepsilon$



This way $x$ and $x^R$ are simultanously generated with the start symbol $S$ in the middle. After that $S$ changes to $A$ in order to produce some word $y$ between $x$ and $x^R$.

* * *

Edit: As was pointed out, the language is just $\\{a,b\\}^*$, so there is a simpler grammar (see the other answer).