Solution

The correct answer is R = QP*.

Key Points

• Given equation in regular expressions: R = Q + RP
• This is a standard linear equation of the form: X = A + XB
• By Arden’s Theorem: If B does not contain ε, then the unique solution is X = AB*.
• Comparing terms: X → R, A → Q, B → P.
• Therefore the solution becomes: R = QP*.

Additional Information

• Arden’s Theorem:
  • If X = A + XB and ε ∉ B, then X = AB*.
  • Used to solve regular expression equations in automata theory.
• Important Points:
  • Condition ε ∉ P guarantees unique solution.
  • This theorem is widely used in DFA → RE conversions.