Consider the following expression grammar. The seman­tic rules for expression calculation are stated next to each grammar production.

$$\eqalign{ & E \to number\,\,\,\,\,E.val = number.val \cr & \,\,\,\,\,\,\,\,\,\,\,|E\,\,' + '\,\,E\,\,\,\,\,\,{E^{\left( 1 \right)}}.val = {E^{\left( 2 \right)}}.val + {E^{\left( 3 \right)}}.val \cr & \,\,\,\,\,\,\,\,\,\,\,|\,E\,\,' \times '\,\,E\,\,\,\,\,\,\,{E^{\left( 1 \right)}}.val = {E^{\left( 2 \right)}}.val \times {E^{\left( 3 \right)}}.val \cr} $$

Assume the conflicts in the previous question are resolved and an LALR(1) parser is generated for parsing arithmetic expressions as per the given grammar. Consider an expression
3 × 2 + 1.
What precedence and associativity properties does the generated parser realize?

Which of the following grammar rules violate the requirements of an operator grammar? P, Q, R are nonterminals, and r, s, t are terminals.

$$\eqalign{ & 1.\,P \to QR \cr & 2.\,P \to QsR \cr & 3.\,P \to \varepsilon \cr & 4.\,P \to QtRr \cr} $$

Consider the grammar with the following translation rules and E as the start symbol.

$$\eqalign{ & E \to {E_1}\# T\,\,\left\{ {E.value = {E_1}.value*T.value} \right\} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,|T\,\,\,\,\,\,\,\,\,\,\,\,\left\{ {E.value = T.value} \right\} \cr & T \to {T_1}\& F\,\,\,\left\{ {T.value = {T_1}.value*F.value} \right\} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,|\,F\,\,\,\,\,\,\,\,\,\,\,\left\{ {T.value = F.value} \right\} \cr & F \to num\,\,\,\,\,\,\,\left\{ {F.value = num.value} \right\} \cr} $$

Compute E.value for the root of the parse tree for the expression:
2 # 3 & 5 # 6 & 4.

Consider the grammar shown below

$$\eqalign{ & S \to iEtSS'\,|\,\,a \cr & S' \to eS\,|\,\,\varepsilon \cr & E \to b \cr} $$

In the predictive parse table, $$M$$, of this grammar, the entries $$M\left[ {S',e} \right]$$ and $$M\left[ {S',\phi } \right]$$ respectively are