[Solved]: Create CFG and pushdown automaton for {ww}

Problem Detail: 

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 $w = aba$.

Asked By : AaoIi

Answered By : Raphael

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

See our reference questions for how to prove that, i.e.

• How to prove that a language is not regular?
• How to prove that a language is not context-free?

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/37280