Consider the alphabet βˆ‘ = {0, 1}, the null/empty string πœ† and the sets of…

GATE Β· 2015 Β· CS Β· Set 2 Β· Computer Science & IT

Consider the alphabet βˆ‘ = {0, 1}, the null/empty string πœ† and the sets of strings X0, X1, and X2 generated by the corresponding non-terminals of a regular grammar. X0, X1, and X2 are related as follows.

X0 = 1 X1

X1 = 0 X1 + 1 X2

X2 = 0 X1 + {πœ†}

Which one of the following choices precisely represents the strings in X0?

  1. A.

    10(0* + (10)*)1

  2. B.

    10(0* + (10)*)*1

  3. C.

    1(0 + 10)*1

  4. D.

    10(0 + 10)*1 + 110(0 + 10)*1

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Correct answer: C

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