DFA construction

Question

Design a DFA (Deterministic Finite Automaton) that recognizes the language L defined follows:

L= {w -> {a, b}* | every a in w is immediately followed by bb}

Answer 1

In eyery string a must followed bb substring so the language accepted by the machine is l={abb,abbb,abbbbb,abbabb...}

now minimum length of the string is = 3

required no fo statesw = 3+1 = 4

               a               b

q0         q1               dead

q1         dead             q2

q2          dead            q3

q3          q1                 q3