In the ε-NFA, M = ({q₀, q_1, q_2, q₃}, {a}, δ, q0, {q3}) where 'δ' is given in the transition table below, what is the minimum length of string to reach to the final state?

	ε	a
q0	{q1}	{}
q1	{q2}	{}
q2	{}	{q2, q3}
q3	{}	{}

The correct answer is option 2) 1

Key Points

• An ε-NFA or epsilon-NFA is a type of non-deterministic finite automaton that includes epsilon or empty string transitions.

• To find the minimum length of a string to reach the final state in the given ε-NFA, you can analyze the transitions and the epsilon (ε) transitions. The ε-NFA has states q0, q1, q2, and q3.
• Starting from the initial state q0, you need to follow the transitions and epsilon transitions until you reach the final state q3. Let's go step by step:
  • Start at q0.
  • Use the ε-transition to go from q0 to q1.
  • Use the ε-transition to go from q1 to q2.
  • Use the 'a' transition to go from q2 to q3.
• Now, you have reached the final state q3. The minimum length of the string to reach q3 is 1, as there is one 'a' transition from q2 to q3.
• Therefore, the minimum length of the string to reach the final state q3 is 1.