GATE | GATE CS 1999 | Question 40

A grammar that is both left and right recursive for a non-terminal is
(A) Ambiguous
(B) Unambiguous
(C) Information is not sufficient to decide whether it is ambiguous or Unambiguous.
(D) None of the above


Answer: (C)

Explanation: Suppose we have grammar like this :

S → n
B → BbB 

Here we see that grammar is left as well as right recursive but still it is unambiguous grammar because A is useless production but it is still part of grammar.
So we can say that a grammar having both left as well as right recursion may or may not be ambiguous .

Lets understand with another example as we have grammar like this A→AA using this grammar we can not produce any string in finite steps as language of this grammar is empty set {}.
Hence, we finally get conclusion as if grammar is having both left as well as right recursion, then grammar may or may not be ambiguous.

Option (C) is correct.

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