Construct minimal DFA over ∑={a,b} which accepts L={a power n and b power n | n, m>=1}

SOLUTION:

∑={a,b}

L =  {ab, aab, abb, aabb, aaabb, …….. }

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

1)Transition diagram:

   2)Transition Table:

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

  3)Transition function:

δ( q₀, a)= q₁     ,δ (q₀,b)= D

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

δ( q₂, a)= D     ,δ (q₂,b)= q₂

δ( D, a)= D      ,δ (D, b)= D