Question: If L is a language accepted by some automaton M, which of the following is (are) true?
I. If M is a nondeterministic finite automaton, then L is accepted by some deterministic finite automaton.
II. If M is a deterministic pushdown automaton, then L is accepted by some nondeterministic pushdown automaton.
III. If M is a nondeterministic pushdown automaton, then L is accepted by some deterministic Turing machine.
A: III only
B: I and II only
C: II and III only
D: I, II, and III
Please eliminate two incorrect options first, then think it step by step and choose the most proper one option. Give two different versions of responses. Please separate the responses with 6 asterisk symbols: ******.
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