Finite State Automation (DFA) Contains With |Examples|

1. Construct finite state automata (DFA) that contains with abb

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

Q: set of all states (q_0, q_1, q_2, q₃)
F: Final State 

 Transition Matrix

		f
		a	b
ε	q0	q1	q0
a	q1	q1	q2
ab	q2	q1	q3
abb	q3	q3	q3

Transition Graph

2. Construct finite state automata (DFA) that contains with aab

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

Q: set of all states (q_0, q_1, q_2, q₃)
F: Final State 

  Transition Matrix

		f
		a	b
ε	q0	q1	q0
a	q1	q2	q0
ab	q2	q2	q3
abb	q3	q3	q3

Transition Graph

3. Construct finite state automata (DFA) that contains with aba

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

Q: set of all states (q_0, q_1, q_2, q₃)
F: Final State 

  Transition Matrix

		f
		a	b
ε	q0	q1	q0
a	q1	q1	q2
ab	q2	q3	q0
abb	q3	q3	q3

Transition Graph

4. Construct finite state automata (DFA) that contains with aabb

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

Q: set of all states (q_0, q_1, q_2, q₃)
F: Final State 

  Transition Matrix

		f
		a	b
ε	q0	q1	q0
a	q1	q2	q0
aa	q2	q2	q3
aab	q3	q1	q4
aabb	q4	q4	q4

Transition Graph