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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}
 
Q. 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
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider alphabet ∑ = {0, 1}, the null/empty string λ and t...
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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Consider alphabet ∑ = {0, 1}, the null/empty string λ and the sets of strings X0, X1and X2generated by the corresponding non-terminals of a regular grammar. X0, X1and X2are related as follows:X0 = 1 X1X1 = 0 X1 + 1 X2X2 = 0 X1 + {λ}Q.Which one of the following choices precisely represents the strings in X0?a)10 (0* + (10)*)1b)10 (0* + (10)*)*1c)1(0* + 10)*1d)10 (0 + 10)*1 + 110 (0 + 10)*1Correct answer is option 'C'. Can you explain this answer?
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