GATE | GATE-CS-2016 (Set 1) | Question 27

Which of the following decision problems are undecidable


(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only


Answer: (C)

Explanation: A problem is undecidable if there is no algorithm to find the solution for it.

Statement-I is disjointness problem of two regular languages are decidable.

Statement-II is membership problem of CFG which is always decidable.

Statement-III is equivalence problem of two Context free grammars (CFGs) which is undecidable.

Statement-IV, Given a Turing Machine M, is L(M) = Ф is well known undecidable problem, i.e., non-RE. But, is L(M) ≠ Ф is semi-decidable, i.e., RE but not REC.

Therefore, only statements III and IV are decidable. Option (C) is correct.

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