UGC-NET | UGC NET CS 2015 Jun – III | Question 21

The transition function for the language L = {w|n_a (w) and n_b(w) are both odd} is given by:
δ (q₀, a) = q₁ ; δ (q₀, b) = q₂
δ (q₁, a) = q₀ ; δ (q₁, b) = q₃
δ (q₂, a) = q₃ ; δ (q₂, b) = q₀
δ (q₃, a) = q₂ ; δ (q₃, b) = q₁
The initial and final states of the automata are:
(A) q₀ and q₀respectively
(B) q₀ and q₁respectively
(C) q₀ and q₂respectively
(D) q₀ and q₃respectively


Answer: (D)

Explanation: Transition diagram for L = {w|n_a (w) and n_b(w) are both odd}:

q₃ satisfies the condition – {w|n_a (w) and n_b(w) are both odd} , so q₃ is final state and all strings starts from q₀ so q₀ is final state.
So, option (D) is correct.

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