GATE | GATE CS 2013 | Question 41

Which of the following is/are undecidable?

(A) 3 only
(B) 3 and 4 only
(C) 1, 2 and 3 only
(D) 2 and 3 only

Answer: (D)


  • First is Emptiness for CFG; whether a CFG is empty or not, this problem is decidable.
  • Second is everything for CFG; whether a CFG will generate all possible strings (completeness of CFG), this problem is undecidable.
  • Third is Regularity for REC; whether language generated by TM is regular is undecidable.
  • Fourth is equivalence for regular; whether language generated by DFA and NFA are same is decidable.

Second and third will be undecidable. Hence, option (D) is Correct.

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