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) = ϕ? 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)?  

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) = ϕ? 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)?   Correct Answer III and IV only

Decidable properties of Languages:

For decidable: D

For un-decidable: U

For grammar: G

From the above table:

Membership property of regular grammar is decidable.

Emptiness problem of context free grammar is decidable.

Universality property for context free grammar is undecidable.

Membership problem of Turing machine is undecidable.