GATE CS 2014 Set 2 Q17 — Parsing (LL, LR)

To determine the associativity of the operators $+$ and $*$, we analyze the recursive structure of the production rules defining them:

1. Associativity of $*$ (defined by $T$):

   The production rule is:

   $$T \to T * U \mid U$$

   This is a left-recursive production because the non-terminal on the left-hand side ($T$) appears as the leftmost symbol on the right-hand side of the recursive alternative ($T * U$). Left-recursion groups operands from left to right, meaning the operator $*$ is left-associative.

2. Associativity of $+$ (defined by $P$):

   The production rule is:

   $$P \to Q + P \mid Q$$

   This is a right-recursive production because the non-terminal on the left-hand side ($P$) appears as the rightmost symbol on the right-hand side of the recursive alternative ($Q + P$). Right-recursion groups operands from right to left, meaning the operator $+$ is right-associative.

Thus, $+$ is right-associative, while $*$ is left-associative.