0
$\begingroup$

The PDA has to recognize the language $L = \{w\in \{a,b,c\}^* \mid |w|_a = |w|_b$ or $ |w|_a=|w|_b\}$.
Currently I have an automaton which recognises that language if $|w_a|=|w|_b$ xor $|w_a|=|w|_c$. It looks like this:PDA

It is xor because it is going to empty the stack before it could check next letter's occurence.
My question is how can I divide this into two PDAs (one recognises $|w|_a=|w|_b$ and the other one recognises $|w|_a=|w|_c$) and take the union of those PDAs?
Or is there any better solution?

$\endgroup$
2
  • $\begingroup$ Do you actually need to produce a PDA? If not, producing a PDA for $\#a=\#b$ is enough, since $\#a=\#c$ is essentially identical and context-free languages are closed under taking unions. Alternatively, nondeterminism is your friend. $\endgroup$ Apr 30, 2017 at 20:26
  • $\begingroup$ Welcome to Computer Science! The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you! $\endgroup$
    – Raphael
    May 1, 2017 at 0:14

1 Answer 1

1
$\begingroup$

actually you also had a mistake in the definition of the problem and I've considered its |Wa|=|Wb| or |Wa|=|Wc|. Any way using non-deterministic I've tried to separate two conditions: NPDA - the upper way specify equality a's & b's and so on

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.