Design DFA for the following languages L={ w |w is any string that does not contain exactly two a’s} over ∑={a,b}

SOLUTION:

∑={a,b}

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

1)Transition diagram:

2)Transition Table:

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

  3)Transition function:

δ( q₀, a)= q₁     ,δ (q₀,b)= q₀   

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

δ( q₂, a)= q₂     ,δ (q₂,b)= q₂