# Create CFG and pushdown automaton for {ww} [duplicate]

I've been trying to make a CFG, a pushdown automaton and a regular expression for the language

$\qquad L(M) = \{ww : w \in \{a, b\}^*, |w| \text{ is even}\}$.

I understand how the reverse of the string work, that is

$\qquad L' = \{ ww^R : w \in \{a, b\}^*\}$,

what i am asking for is to do it this way , i have already solved (L') : http://i921.photobucket.com/albums/ad53/Johann_1990/IMG_20150117_132616.jpg

but is there is a way to solve this one too?
$\qquad L(M) = \{ww : w \in \{a, b\}^*, |w| \text{ is even}\}$.

For example, $abaaba \in L$ with $w = aba$.

## marked as duplicate by D.W.♦, Rick Decker, David Richerby, Luke Mathieson, JuhoJan 17 '15 at 9:58

• Note that $ww = abaaba$ is a bad example (as in, you don't learn anything from it) here as $w = w^R$. – Raphael Jan 16 '15 at 14:58
• @Raphael , i need to train my self for any example.. when i am learning ! i know how to make the reverse of string pushdown or cfg, i was just trying something new! Thank you ! – AaoIi Jan 16 '15 at 20:52
• @D.W.,its not the same question am talking about another thing completely.. – AaoIi Jan 16 '15 at 20:53

You can not do so as $L$ is not context-free.