Constructing PDA for $a^{2n} b^{3n}$

Problem Detail: 

So I have been given the task of creating an PDA that recognises the language

$\{a^{2n} b^{3n} \mid n = 0,1,2,\dots\}$.

Am I right in thinking that it needs to have at least 3 times number of $b$'s than $a$'s?

So for example: $aabbb$ would be accepted $aaabb$ would NOT be accepted However, how do I show that using JFlap because I am unfamiliar with the software?

Asked By : Anish B

Answered By : Dave Clarke

The following pushdown automaton should do the trick. I publish this only because the existing answer can be improved upon. (Note, I am using $e$ to denote $\epsilon$- (or $\lambda$-) transitions.

The idea is that the left-hand part counts the number of $a$'s (modulo 2). Each time it has seen two $a$'s, it pushes $3$ $b$'s onto the stack. Nondeterministically, the machine can change to the right-hand state. It then matches a $b$ from the string fro each $b$ on the stack.

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Question Source : http://cs.stackexchange.com/questions/10423