GATE | GATE CS 2020 | Question 20

Consider the language L = { aⁿ ∣ n≥0 }∪{ aⁿbⁿ ∣ n≥0 } and the following statements.

• I. L is deterministic context-free.
• II. L is context-free but not deterministic context-free.
• III. L is not LL(k) for any k.

Which of the above statements is/are TRUE ?

(A)

Ⅰ only

(B)

Ⅱ only

(C)

Ⅰ and Ⅲ only

(D)

Ⅲ only

Answer: (C)
Explanation:

Language { aⁿ ∣ n≥0 } is regular and { aⁿbⁿ ∣ n≥0 } is deterministic context free language (DCFL), so union of these will be DCFL, because union of DCFL with regular is always DCFL, but may be regular. Every DFCL is always CFL but converse may not true. 
So, statement (I) is true and (II) is false. Statement (III) is also true. 

hence, Option (C) is Correct.

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