GATE | GATE-CS-2015 (Set 2) | Question 45

Consider alphabet ∑ = {0, 1}, the null/empty string λ 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 + {λ} 

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

(A) 10 (0* + (10)*)1
(B) 10 (0* + (10)*)*1
(C) 1(0* + 10)*1
(D) 10 (0 + 10)*1 + 110 (0 + 10)*1


Answer: (C)

Explanation:

The smallest possible string by given grammar is "11".
X0 = 1X1
   = 11X2  [Replacing X1 with 1X2]
   = 11    [Replacing X2 with λ]

The string "11" is only possible with option (C).

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