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Why is the conversion from nondeterministic PDA to deterministic PDA not possible?

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There are languages accepted by nondeterministic PDAs that cannot be accepted by deterministic PDAs. Perhaps the easiest way to see this is to consider inherently ambiguous context-free languages. As context-free languages, they are accepted by some nondeterministic PDA. On the other hand, every language accepted by a deterministic PDA has an unambiguous grammar, so they cannot be accepted by any deterministic PDA.

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