Question

Consider the augmented grammar with \(\{+,* , (, ), id\}\) as the set of terminals. \[ S' \rightarrow S \] \[ S \rightarrow S + R \mid R \] \[ R \rightarrow R^{\,*} P \mid P \] \[ P \rightarrow (S) \mid id \] If \(I_0\) is the set of two LR(0) items \(\{[S' \rightarrow S.], [S \rightarrow S. + R]\}\), then \(goto(\text{closure}(I_0), +)\) contains exactly \(\underline{\hspace{1cm}}\) items.

Hint:

The \(goto\) operation in an LR parser moves to the next state based on a specific terminal or non-terminal. The closure ensures all applicable items are included in the state.

Answer 1

Correct Answer: 5

We start by applying the closure operation on the LR(0) items. The closure of \(I_0\) includes all the items that can be derived from the current items. Initially, we have: \[ I_0 = \{[S' \rightarrow S.], [S \rightarrow S. + R]\}. \] Now, applying the \(goto(\text{closure}(I_0), +)\) operation, we get the following items: \[ [ S \rightarrow S + . R ] \] and \[ [ R \rightarrow R . P ]. \] Thus, the number of items in \(goto(\text{closure}(I_0), +)\) is 5.
Therefore, the number of items is: \[ \boxed{5}. \]