Ace test

Question

DPDA does not closed under equivalence property

i do understand by minimizing the DFA we can say whether they are equal or not

But it is not the case with DPDA so plz someone explain it to me how can (ii) is correct.

Comments

It is not so easy to prove as in the case of DFA. In fact it is so difficult that this problem was solved only very recently and fetched the Godel prize in 2002. 

https://en.wikipedia.org/wiki/Deterministic_pushdown_automaton

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Thank you  sir.