Finite State Automation (DFA) Starts With |Examples|

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 (q_0, q_1, q_2, q_3,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 (q_0, q_1, q_2, q_3,qФ)
F: Final State 

    Transition Matrix

		f
		a	b
ε	p0	p1	qФ
a	p1	p2	qФ
ab	p2	qФ	p3
abb	p3	p3	p3
	p4	qФ	qФ

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 (q_0, q_1, q_2, q_3,qФ)
F: Final State 

    Transition Matrix

		f
		a	b
ε	p0	p1	qФ
a	p1	qФ	p2
ab	p2	p3	qФ
abb	p3	p3	p3
	p4	qФ	qФ

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 (q_0, q_1, q_2, q_3, q_4, qФ)
F: Final State 

    Transition Matrix

		f
		a	b
ε	p0	p1	qФ
a	p1	p2	qФ
aa	p2	qФ	p3
aab	p3	qФ	p4
aabb	p4	p4	p4
	p5	qФ	qФ

Transition Graph