GATE | GATE CS Mock 2018 | Set 2 | Question 50

Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Let L(M) be the language accepted by a Turing machine M. Which of the following decision problems are decidable?

I. Whether L(G) is deterministic context free language?

II. Whether L(G1)∩L(G2) is a context free language, where G1 and G2 are deterministic grammar?

III. Given a context-free grammar G, is L(G)=Σ for some alphabet Σ?

IV. Given a Turing machine M and a string w, is w ∈ L(M)?
(A) III and IV only
(B) II and IV only
(C) I and II only
(D) None of the above

Answer: (D)

Explanation: All are undecidable problem. Option (D) is correct.

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