# GATE | GATE-CS-2001 | Question 18

• Difficulty Level : Easy
• Last Updated : 28 Jun, 2021

Which of the following statements is false?
(A) An unambiguous grammar has same leftmost and rightmost derivation
(B) An LL(1) parser is a top-down parser
(C) LALR is more powerful than SLR
(D) An ambiguous grammar can never be LR(k) for any k

Explanation: 1. A grammar is ambiguous if there exists a string s such that the grammar has more than one leftmost derivations for s. We could also come up with more than one rightmost derivations for a string to prove the above proposition, but not both of right and leftmost. An unambiguous grammar can have different rightmost and leftmost derivations.

2. LL parser is top-down by nature. Leftmost derivation is, intuitively, expanding or top-down in fashion, hence such convention. Rightmost derivation, on the other hand, seems like a compressing or bottom-up thing.

3. LALR is more powerful than SLR, even when both have the same LR(0) states, due to the fact that SLR checks for lookaheads by looking at FIRST and FOLLOW from the grammar after constructing its parse table and on the other hand, LALR computes lookaheads from the LR(0) states while constructing the parse table, which is a better method.

4. An ambiguous grammar can never be LR(k) for any k, because LR(k) algorithm arenâ€™t designed to handle ambiguous grammars. It would get stuck into undecidability problem, if employed upon an ambiguous grammar, no matter how large the constant k is.

This solution is contributed by Vineet Purswani.

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