GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 43

Consider the following finite automata:

Which of the following are FALSE?

1. Complement of L(A) does not accept strings that starting from 'a'.
2. L(A) = {a, b}* - b(a, b)*.
3. DFA for above finite automata has 2 final stats and total 4 states.
4. Minimal DFA has single finale state. 

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


Answer: (A)

Explanation: Minimal DFA for the above finite automata is,

Therefore,

  1. Complement of L(A) is also accept strings that starting from ‘a’.
  2. L(A) = {a, b}* – b(a, b)*.
  3. DFA for above finite automata has 3 final stats and total 4 states. Final states can merge to single state.
  4. Final states can merge to single state in minimal DFA.

So, only statements 1 and 3 are false.

Option (A) is true.

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