In the ε-NFA, M = ({q0, q1, q2, 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 {} {}

This question was previously asked in
UGC NET Computer Science (Paper 2) 11 March 2023 Official Paper
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Answer (Detailed Solution Below)

Option 2 : 1
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
50 Qs. 100 Marks 60 Mins

Detailed Solution

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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.

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