Discussion
Which of the following conversions is not possible algorithmically ?
Answer: D
The conversion that is not possible is Non-deterministic PDA to deterministic PDA.
Non-deterministic pushdown automata accept all context-free languages, but deterministic PDAs accept only the deterministic context-free languages, a proper subset. For example the language of even-length palindromes needs non-determinism, so no algorithm can convert every NPDA into an equivalent DPDA.
The other conversions are always possible: a regular grammar already is a context-free grammar; the subset construction converts an NFA to a DFA; and a deterministic Turing machine can simulate a non-deterministic one by trying all branches.
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