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# GATE | GATE CS 1997 | Question 45

Which one of the following is not decidable?
(A) Given a Turing machine M, a string s and an integer k, M accepts s within k steps
(B) Equivalence of two given Turing machines
(C) Language accepted by a given finite state machine is not empty
(D) Language generated by a context free grammar is non-empty

Explanation:

• (A) This is decidable because given a Turing machine M, a string s and an integer k, M accepts s within k steps is either halt or not but it will decide within k steps.
• (B) Equivalence of two Turing machines are undecidable because Recursive Enumerable languages are not closed under complement.
• (C) Language accepted by a given finite state machine is not empty is definitely decidable, since we can always minimize the DFA and see whether itâ€™s a single state with no accepting state
• (D) Language generated by a context free grammar is non-empty is also decidable for this we have algorithm.

Option (B) is correct.

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