Construct a DFA, that accepts set of all strings over ∑={a,b} of length at most 2 i.e. |w|<=2

SOLUTION:

∑={a,b}

L = {All the strings of length at most 2 }

L = {∈, a, b, aa, ab, ba, bb}

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

  3)Transition function:

δ( q₀, a)= q₁     ,δ (q₀,b)= q₁    

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

δ( q₂, a)= D     ,δ (q₂,b)= D

δ( D, a)= D      ,δ (D, b)= D