GATE CS 2001 Q1.18 — Parsing (LL, LR)

To find the false statement, let's analyze each option:

• Option A: An unambiguous grammar guarantees that every valid string has a unique leftmost derivation (LMD) and a unique rightmost derivation (RMD). However, the LMD and RMD themselves are generally different sequences of derivation steps. For example, for the unambiguous grammar $S \to AB$, $A \to a$, $B \to b$, the LMD is $S \Rightarrow AB \Rightarrow aB \Rightarrow ab$, while the RMD is $S \Rightarrow AB \Rightarrow Ab \Rightarrow ab$. Since these derivations are different, this statement is false.
• Option B: LL(1) is a predictive top-down parsing technique. This statement is true.
• Option C: LALR(1) uses lookahead propagation to resolve conflicts that SLR(1) cannot, making LALR strictly more powerful than SLR. This statement is true.
• Option D: Every LR(k) grammar is deterministic and therefore must be unambiguous. Thus, an ambiguous grammar can never be LR(k) for any $k$. This statement is true.