Design DFA to accepts L , where L is set of strings in which 'a' always appears tripled over ∑={a,b}

SOLUTION:

∑={a,b}

L = {aaa, aaab, baaa, baaab, bbaaa,……… }

Ø  So DFA can be Q={ q₀ , q₁ , q₂ ,q₃ },∑={a,b}, q₀={ q₀},F={q₃} 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	D
q2	q3	D
*q3	q1	q3
D	D	D

  3)Transition function:

δ( q₀, a)= q₁     ,δ (q₀,b)= q₀

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

δ( q₂, a)= q₃     ,δ (q₂,b)= D

δ( q₃, a)= q₁     ,δ (q₂,b)= q₃

δ( D, a)= D      ,δ (D, b)= D