List of top Compiler Design Questions on Syntax Directed Translation asked in GATE CS

Consider the following two syntax-directed definitions SDD1 and SDD2 for type declarations.
SDD1
Grammar (G1): \(D \rightarrow T\,V\); Semantic Rules: \(D.type = T.type;\ V.type = T.type\)
Grammar (G1): \(T \rightarrow int\); Semantic Rules: \(T.type = int\)
Grammar (G1): \(T \rightarrow float\); Semantic Rules: \(T.type = float\)
Grammar (G1): \(V \rightarrow V_1\,id\); Semantic Rules: \(V_1.type = V.type;\ put(id.entry, V.type)\)
Grammar (G1): \(V \rightarrow id\); Semantic Rules: \(put(id.entry, V.type)\)
SDD2
Grammar (G2): \(D \rightarrow D_1\,id\); Semantic Rules: \(D.type = D_1.type;\ put(id.entry, D_1.type)\)
Grammar (G2): \(D \rightarrow T\,id\); Semantic Rules: \(D.type = T.type;\ put(id.entry, T.type)\)
Grammar (G2): \(T \rightarrow int\); Semantic Rules: \(T.type = int\)
Grammar (G2): \(T \rightarrow float\); Semantic Rules: \(T.type = float\)
\(D\) is the start symbol, and \(int\), \(float\) and \(id\) are the three terminals. The non-terminal \(V_1\) is the same as \(V\) and the non-terminal \(D_1\) is the same as \(D\). Here, the subscript is used to differentiate the grammar symbols on the two sides of a production. The function \(put\) updates the symbol table with the type information for an identifier.
Let P and Q be the languages specified by grammars G1 and G2, respectively.
Which of the following statements is/are true?

Given the following syntax directed translation rules: 
Rule 1: \( R \to AB \) { \( B.i = R.i - 1 \); \( A.i = B.i \); \( R.i = A.i + 1 \); } 
Rule 2: \( P \to CD \) { \( P.i = C.i + D.i \); \( D.i = C.i + 2 \); } 
Rule 3: \( Q \to EF \) { \( Q.i = E.i + F.i \); } 
Which ONE is the CORRECT option among the following?

The number of distinct minimum-weight spanning trees of the following graph is ............ \begin{center} \includegraphics[width=0.5\textwidth]{59.png} \end{center}
Consider the following augmented grammar, which is to be parsed with an SLR parser. The set of terminals is \(\{a, b, c, d, \#, @\}\). \[ S' \rightarrow S \quad S \rightarrow SS \, | \, Aa \, | \, bAc \, | \, BC \, | \, bBa \quad A \rightarrow d\# \quad B \rightarrow @ \] Let \(I_0 = \text{CLOSURE}(\{S' \rightarrow \cdot S\}\). The number of items in the set \(GOTO(I_0, S)\) is ............
Consider the following expression: \(x[i] = (p + r) * -s[i] + u / w\). The following sequence shows the list of triples representing the given expression, with entries missing for triples (1), (3), and (6). \begin{center} \begin{tabular}{|c|c|c|c|} \hline (0) & \(+\) & \(p\) & \(r\)
\hline (1) & & &
\hline (2) & \texttt{uminus} & \((1)\) &
\hline (3) & & &
\hline (4) & \(/\) & \(u\) & \(w\)
\hline (5) & \(+\) & \((3)\) & \((4)\)
\hline (6) & & &
\hline (7) & \(=\) & \((6)\) & \(x[i]\)
\hline \end{tabular} \end{center} Which one of the following options fills in the missing entries CORRECTLY?
Consider the following context-free grammar where the start symbol is \(S\) and the set of terminals is \(\{a, b, c, d\}\): \[ S \to AaAb \, | \, BbBa \quad \quad A \to cS \, | \, \epsilon \quad \quad B \to dS \, | \, \epsilon \] The following is a partially-filled LL(1) parsing table. \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline & \(a\) & \(b\) & \(c\) & \(d\) & \(\$\)
\hline \(S\) & \(S \to AaAb\) & \(S \to BbBa\) & (1) & (2) &
\hline \(A\) & \(A \to \epsilon\) & (3) & \(A \to cS\) & &
\hline \(B\) & (4) & \(B \to \epsilon\) & & \(B \to dS\) &
\hline \end{tabular} \end{center} Which one of the following options represents the CORRECT combination for the numbered cells in the parsing table? Note: In the options, "blank" denotes that the corresponding cell is empty.}
Let \(A\) be an array containing integer values. The distance of \(A\) is defined as the minimum number of elements in \(A\) that must be replaced with another integer so that the resulting array is sorted in non-decreasing order. The distance of the array \([2, 5, 3, 1, 4, 2, 6]\) is ...........\_\_\_.
Consider the following two sets: \begin{center} \begin{tabular}{|c|l|c|l|} \hline Set X & & Set Y &
\hline P. & Lexical Analyzer & 1. & Abstract Syntax Tree
Q. & Syntax Analyzer & 2. & Token
R. & Intermediate Code Generator & 3. & Parse Tree
S. & Code Optimizer & 4. & Constant Folding
\hline \end{tabular} \end{center} Which one of the following options is the CORRECT match from Set X to Set Y?