GATE | GATE CS 2018 | Question 50

Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M.

(I) For an unrestricted grammar G and a string w, whether wϵL(G)
(II) Given a Turing machine M, whether L(M) is regular
(III) Given two grammar G₁ and G₂, whether L(G₁) = L(G₂)
(IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language

Which one of the following statement is correct?
(A) Only I and II are undecidable
(B) Only II is undecidable
(C) Only II and IV are undecidable
(D) Only I, II and III are undecidable

Answer: (D)
Explanation: I, II and III are undecidable, refer this:

Coming to IV, every regular language is Deterministic-CFL, which is a trivial property.

Option (D) is Correct.

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