Discussion
Which one of the following is not decidable ?
Answer: B
The problem that is not decidable is the equivalence of two given Turing machines.
Whether two Turing machines accept the same language is undecidable; if it were decidable, we could decide whether a machine accepts the empty language by comparing it with a machine that rejects everything, which contradicts Rice's theorem.
The others are decidable: whether M accepts S within K steps is settled by simulating M for K steps; emptiness of a DFA's language is checked by searching for a path from the start state to an accepting state; and emptiness of a CFG's language is checked by finding whether the start symbol can derive a terminal string.
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