GATE | GATE CS 2013 | Question 33

Consider the DFA given.

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Which of the following are FALSE?

1. Complement of L(A) is context-free.
2. L(A) = L((11*0+0)(0 + 1)*0*1*)
3. For the language accepted by A, A is the minimal DFA.
4. A accepts all strings over {0, 1} of length at least 2. 

(A) 1 and 3 only
(B) 2 and 4 only
(C) 2 and 3 only
(D) 3 and 4 only


Answer: (D)

Explanation: 1 is true. L(A) is regular, its complement would also be regular. A regular language is also context free.

2 is true.

3 is false, the DFA can be minimized to two states. Where the second state is final state and we reach second state after a 0.

4 is clearly false as the DFA accepts a single 0.

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