GATE CS 2012 Q53 — Parsing (LL, LR)

For the grammar below, a partial $LL(1)$ parsing table is also presented along with the grammar. Entries that need to be filled are indicated as $E1, E2,$ and $E3$. $\varepsilon$ is the empty string, \$ indicates end of input, and, $\mid$ separates alternate right hand sides of productions.

• $S \rightarrow a A b B \mid b A a B \mid \varepsilon$
• $A \rightarrow S$
• $B \rightarrow S$

$$\begin{array}{|l|l|}\hline \text{} & \textbf{a} & \textbf{b} & \textbf{\$} \\ \hline \text{$S$} & \text{E1} & \text{E2} & \text{$S\rightarrow \varepsilon $} \\ \hline \text{$A$} & \text{$A\rightarrow S$} & \text{$A\rightarrow S$} & \text{error} \\ \hline \text{$B$} & \text{$B\rightarrow S$} & \text{$B\rightarrow S$} & \text{$E3$} \\ \hline \end{array}$$The appropriate entries for $E1, E2,$ and $E3$ are