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Consider the finite automaton in the following figure:

 

What is the set of reachable states for the input string $0011$?

  1. $\{q_0,q_1,q_2\}$
  2. $\{q_0,q_1\}$
  3. $\{q_0,q_1,q_2,q_3\}$
  4. $\{q_3\}$
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$q_0, q_1$ and $q_2$ are reachable from $q_0$ on input $0011$

Correct Answer: $A$

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{q0 , 0 → q0} , { q0 , 0 → q0 }, {q0 , 1 → q0}, {q0 , 1 → q0} . Hence δ (q0, 0011) = q0
 

{q0 , 0 → q0} , { q0 , 0 → q0 }, {q0 , 1 → q0}, {q0 , 1 → q1} . Hence δ (q0, 0011) = q1
 

{q0 , 0 → q0} , { q0 , 0 → q0 }, {q0 , 1 → q1}, {q1 , 1 → q2} . Hence δ (q0, 0011) = q2
 

Hence δ (q0, 0011) = {q0, q1, q2}

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{q0 , 0 → q0} , { q0 , 0 → q0 }, {q0 , 1 → q0}, {q0 , 1 → q0} . Hence δ (q0, 0011) = q0
{q0 , 0 → q0} , { q0 , 0 → q0 }, {q0 , 1 → q0}, {q0 , 1 → q1} . Hence δ (q0, 0011) = q1
{q0 , 0 → q0} , { q0 , 0 → q0 }, {q0 , 1 → q1}, {q1 , 1 → q2} . Hence δ (q0, 0011) = q2
Hence δ (q0, 0011) = {q0, q1, q2}

Answer:

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