UGC NET Computer Science December 2019 | Question 94

Question 94

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Consider the language L = {aⁿ b^n-3 | n > 2} on Σ = {a, b}. Which one of the following grammars generates the language L?

1. (1) S→aA|a, A→aAb|b
2. (2) S→aaA|λ, A→aAb|λ
3. (3) S→aaaA|a, A→aAb| λ
4. (4) S→aaaA, A→aAb|λ

Answer : (4) S→aaaA, A→aAb|λ

Explanation

Option 1 is incorrect because it can generate “a” where n = 1. so given condition (n > 2) is violated.

Option 2 is incorrect because it can generate “null string”. so given condition (n > 2) is violated.

Option 3 is incorrect because it can generate “a” where n=1. so given condition (n > 2) is violated.

Option 4 is correct because it can generate strings ab, aaa, aaaab, ... where n > 2.

So, option 4 is correct answer

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