Question 44

The canonical set of items is:

1. $S \to L . > R$
2. $Q \to R .$

Examine possible actions on input symbol '$<$':

1. Shift action:

   • In $S \to L . > R$, the dot is immediately followed by the terminal symbol '$>$'.
   • A shift action in this item is valid only on input symbol '$>$', which transitions to a state containing $S \to L > . R$.
   • There is no shift action on '$<$'.

2. Reduce action:

   • In $Q \to R .$, the dot is at the end of the production, representing a reduction by $Q \to R$.
   • Even if '$<$' is in $\text{FOLLOW}(Q)$ so that a reduction action is placed under '$<$', there is only one reduce item.

3. Conflicts on '$<$':

   • Shift-reduce conflict requires at least one shift and at least one reduce on the same symbol '$<$'. Since there is no shift on '$<$', no shift-reduce conflict exists.
   • Reduce-reduce conflict requires two distinct reduce items to reduce on '$<$'. Since there is only one reduce item in the set, no reduce-reduce conflict can exist.

Therefore, on input symbol '$<$', the set has neither a shift-reduce nor a reduce-reduce conflict.