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 regalur 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.

Option (C) is true.

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