GATE 2017 CSE & IT Q41

Question

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 undecidable?
I. Given a regular expression R and a string w, is w∈ L(R)?
II. Given a context-free grammar G, is L(G) = Ø ?
III. Given a context-free grammar G, is L(G) = ∑* for some alphabet ∑ ?
IV. Given a Turing machine M and a string w, is w∈ L(M)?

Accepted Answer

4

Answer

I and IV only

Answer

II and III only

Answer

II, III and IV only

Answer

III and IV only