Finite State Automation (DFA) Ends With |Examples|

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

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

Transition Graph

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

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

Transition Graph

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

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

Transition Graph

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

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

         q₄ = string ends with aabb

Q: set of all states (q_0, q_1, q_2, q_3, q4)

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	q1	q0

Transition Graph