# Proof $\{u\colon |u| \text{ is odd and$b$is in the middle}\}$ is not deterministic

Without using pumping lemma for deterministic context-free languages I need to prove that the language $\{u\colon |u| \text{ is odd and$b$is in the middle}\}$ is not deterministic.

Someone suggested me that I could try to deduce that if it were deterministic then the language $\{a^nb^nc^n\colon n\ge0\}$ would be context-free. But I don't really see how to use it.

• What kind of argument are you allowed to use? – Yuval Filmus Jan 23 '16 at 17:35
• @Yuval Filmus just some argument that does not use pumping lemma – Rodrigo Jan 23 '16 at 17:41
• Well, you can include a proof of the pumping lemma and then you're fine. – Yuval Filmus Jan 23 '16 at 17:44
• Take a look at the technique suggested here: cs.stackexchange.com/a/38476/683. – Yuval Filmus Jan 23 '16 at 17:55
• Once you have a proof, please answer your own question. – Yuval Filmus Jan 24 '16 at 21:33