Create CFG and pushdown automaton for {ww}

Question

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

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

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 $w = aba$.

score 1 · Accepted Answer · edited Apr 13 '17 at 12:48

1

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

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

edited Apr 13 '17 at 12:48

Community

answered Jan 16 '15 at 12:30

Raphael

1 Answers1