Let P and Q be two regular expressions over Σ . If P does not contain ε, then…

2026

Let P and Q be two regular expressions over Σ . If P does not contain ε, then the following equation in R namely,

R = Q + RP

has a unique solution given by,

  1. R = Q* P*

  2. R = Q P*

  3. R = P Q*

  4. R = Q* + P* R

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

Attempted by 102 students.

Show answer & explanation

Correct answer: B

To solve the equation R = Q + RP for R, we apply Arden's Lemma.

Arden's Lemma states that if P and Q are regular expressions over Σ, and P does not contain ε, then the equation R = Q + RP has a unique solution given by R = QP*.

In the given problem, P does not contain ε, satisfying the condition. Therefore, the unique solution is R = QP*.

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