GATE CS 2014 Set 2 Q.27 (CS Q.17): Parsing and Syntax Analysis (LL and LR)

Consider the grammar defined by the following production rules, with two operators $*$ and $+$

\begin{aligned} S &\longrightarrow T * P \\ T &\longrightarrow U \mid T * U \\ P &\longrightarrow Q + P \mid Q \\ Q &\longrightarrow Id \\ U &\longrightarrow Id \end{aligned}

Which one of the following is TRUE?

$+$ is left associative, while $*$ is right associative

$+$ is right associative, while $*$ is left associative

Both $+$ and $*$ are right associative

Both $+$ and $*$ are left associative

Official answer and solution

Solution

Analyze the grammar productions for left-recursion and right-recursion associated with each operator.

Production Rules for $*$ :
$T \longrightarrow U \mid T * U$
In the recursive rule $T \longrightarrow T * U$ , the non-terminal $T$ appears as the leftmost symbol on the right-hand side. This is left recursion, which enforces left associativity for operator $*$ .
Production Rules for $+$ :
$P \longrightarrow Q + P \mid Q$
In the recursive rule $P \longrightarrow Q + P$ , the non-terminal $P$ appears on the right of $+$ . This is right recursion, which enforces right associativity for operator $+$ .
Conclusion:
$+$ is right associative, while $*$ is left associative, which corresponds to option (B).

Final answer

Common trap

Assuming standard arithmetic associativity rules instead of reading the recursion structure directly from the grammar.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.