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GATE | GATE CS 1997 | Question 45

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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

Answer: (B)

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 it’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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Last Updated : 10 May, 2020
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