1.  Construct finite state automation (DFA) that starts with 'abb'. 

Solution :
Σ: inputs = {a, b}
          q0 = initial state
          q1 = string starts with a
          q2 = string starts with ab
          q3 = string starts with abb

Q: set of all states (q0, q1, q2, q3,qФ)
F: Final State 

    Transition Matrix
  f
    a b
ε p0 p1 qФ
a p1 qФ p2
ab p2 qФ p3
abb p3 p3 p3

p4 qФ qФ
Transition Graph

2.  Construct finite state automation (DFA) that starts with 'aab'. 

Solution :
Σ: inputs = {a, b}
          q0 = initial state
          q1 = string starts with a
          q2 = string starts with aa
          q3 = string starts with aab

Q: set of all states (q0, q1, q2, q3,qФ)
F: Final State 

    Transition Matrix
f
ab
εp0p1qФ
ap1p2qФ
abp2qФp3
abbp3p3p3

p4qФqФ
Transition Graph

3.  Construct finite state automation (DFA) that starts with 'aba'. 

Solution :
Σ: inputs = {a, b}
          q0 = initial state
          q1 = string starts with a
          q2 = string starts with ab
          q3 = string starts with aba

Q: set of all states (q0, q1, q2, q3,qФ)
F: Final State 

    Transition Matrix
f
ab
εp0p1qФ
ap1qФp2
abp2p3qФ
abbp3p3p3

p4qФqФ
Transition Graph


4.  Construct finite state automation (DFA) that starts with ''. 

Solution :
Σ: inputs = {a, b}
          q0 = initial state
          q1 = string starts with a
          q2 = string starts with aa
          q3 = string starts with aab
          q4 = string starts with aabb

Q: set of all states (q0, q1, q2, q3q4, qФ)
F: Final State 

    Transition Matrix
f
ab
εp0p1qФ
ap1p2qФ
aap2qФp3
aabp3qФp4
aabbp4p4p4

p5 qФ qФ
Transition Graph