Which of the following is an unambiguous grammar that is not...

Which of the following is an unambiguous grammar that is not LR (1)? (A) $S \rightarrow \mathrm{Uab} \mid \mathrm{Vac}$ $U \rightarrow d$ $V \rightarrow d$ (B) $S \rightarrow \mathrm{Uab} / \mathrm{Vab} / \mathrm{Vac}$ $U \rightarrow d$ $V \rightarrow d$ (C) $S \rightarrow A B$ $A \rightarrow a$ $B \rightarrow b$ (D) $S \rightarrow A b$ $A \rightarrow a / c$

Which of the following is an unambiguous grammar that is not LR (1)?
(A) $S \rightarrow \mathrm{Uab} \mid \mathrm{Vac}$
$U \rightarrow d$
$V \rightarrow d$
(B) $S \rightarrow \mathrm{Uab} / \mathrm{Vab} / \mathrm{Vac}$
$U \rightarrow d$
$V \rightarrow d$
(C) $S \rightarrow A B$
$A \rightarrow a$
$B \rightarrow b$
(D) $S \rightarrow A b$
$A \rightarrow a / c$

Key Concepts

LR(1) Grammars

An LR(1) grammar is one that can be parsed using a bottom?up parser which makes decisions based on a single lookahead symbol. This class of grammars is desirable because it allows for deterministic parsing, meaning that at each step the parser can decide uniquely whether to shift, reduce, or accept the input without backtracking.

Unambiguous Grammars

An unambiguous grammar is one in which every string belonging to the language has exactly one parse tree (or derivation). This property is important because it ensures that the structure of the input is interpreted in only one, clear way, eliminating the possibility of multiple conflicting interpretations.

Reduce-Reduce Conflicts

A reduce-reduce conflict arises during the construction of an LR parsing table when, in a given parser state, there are two or more completed productions (reductions) that are applicable for the same lookahead symbol. These conflicts prevent the parser from making a unique choice, and even if the grammar is unambiguous, such conflicts can make it non-LR(1).

Lookahead in Parsing

The use of lookahead in parsing involves examining the next input symbol to decide which production to apply at a given point. In LR(1) parsing, the ‘1’ refers to the use of a single lookahead symbol, and ensuring that this one symbol is enough to resolve any ambiguities or conflicts is key to whether a grammar falls into the LR(1) class.

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