Question

Find the number of final states in DFA that recognizes L, where L= {w1a w2:|w1|≥3,|w2|≤5}, ∑={a, b} and w1, w2 ∈ ∑ * ______

Answer 1

The DFA will be made as follows:

So we accept any number of {a, b} greater than 3, then we wait until we get the ‘a’. After that accept any {a, b} upto count of 5 but not more than 5. Notice q10 is a trap state.

Answer: Hence we have 6 final states.

Comments

But this is rejecting:

aaaa a bbbbb.... this should be valid string 

OR 
 

we are supposed to assume that 

aaa a abbbbb

..since string is rejected ?