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

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

The above grammar and the semantic rules are fed to a yacc tool (which is an LALR (1) parser generator) for parsing and evaluating arithmetic expressions. Which one of the following is true about the action of yacc for the given grammar?

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.

$$\eqalign{ & S \to CC \cr & C \to cC\,|\,d \cr} $$

This grammar is