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GATE 2021 CS (CS2) – Question 19

Theory of Computation · Regular Expressions and Finite Automata · 1 mark · Multiple choice

Regular L⊆{0,1}* has a minimal DFA with k states. Which language necessarily also has a minimal DFA with k states?

  1. L−{01}
  2. L∪{01}
  3. {0,1}*−L
  4. L·L

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Show answer and explanation

Correct answer: (C) {0,1}*−L

Explanation

For a complete DFA, exchanging accepting and nonaccepting states recognizes the complement. State distinguishability is preserved because any suffix separating two states before complementation still separates them afterwards. Thus the complement’s minimal DFA has exactly k states, C.

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