Design DFA for the following languages L={w |w contains neither substring ab or ba} over ∑={a,b}

SOLUTION:

∑={a,b}

Ø  So DFA can be Q={ q₀ , q₁ , q₂ ,q₃ ,q₄ },∑={a,b }, q₀={ q₀},F={ q₀ , q₁, q₃ } and δ is given by the table

1)Transition diagram:

   2)Transition Table:

Present State	Next State
	Input a	Input b
à *q0	q3	q1
*q1	q2	q1
*q3	q3	q4

  3)Transition function:

δ( q₀, a)= q₃     ,δ (q₀,b)= q₁   

            δ( q₁, a)= q₂     ,δ (q₁,b)= q₁   

δ( q₃, a)= q₃     ,δ (q₂,b)= q₄