Compiler Design

Consider the following grammar along with translation rules.
\begin{aligned} &S \rightarrow S_1 \# T & & \{S._{val}=S_{1.val}*T._{val} \} \\ &S \rightarrow T & & \{S._{val}=T._{val} \} \\ &T \rightarrow T_1 \% R & & \{T._{val}=T_{1.val} \div R._{val} \} \\ &T \rightarrow R & & \{T._{val}=R._{val} \} \\ &R \rightarrow id & & \{R._{val}=id._{val} \} \\ \end{aligned}
Here \# and \% are operators and id is a token that represents an integer and id_{.val} represents the corresponding integer value. The set of non-terminals is \{S,T,R,P \} and a subscripted non-terminal indicates an instance of the non-terminal.
Using this translation scheme, the computed value of S_{.val} for root of the parse tree for the expression 20 \# 10 \% 5 \# 8 \% 2 \% 2 is

Consider the augmented grammar with \{+, *, (, ), id \} as the set of terminals.
\begin{aligned}&S' \rightarrow S \\ &S \rightarrow S+R|R \\ &R \rightarrow R*P|P \\ &P \rightarrow (S)|id \end{aligned}
If I_0 is the set of two LR(0) items \{ [S' \rightarrow S.], [S \rightarrow S.+R] \}, then goto(closure(I_0 ),+) contains exactly ______ items.

Which one of the following statements is TRUE?

Consider the following augmented grammar with \{ \#, @, <, >, a, b, c \} as the set of terminals.

\begin{array}{l} S' \rightarrow S \\ S \rightarrow S \# cS \\ S \rightarrow SS \\ S \rightarrow S @ \\ S \rightarrow < S > \\ S \rightarrow a \\ S \rightarrow b \\ S \rightarrow c \end{array}

Let I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\}). The number of items in the set \text{GOTO(GOTO}(I_0 \lt ), \lt ) is ___________

For a statement S in a program, in the context of liveness analysis, the following sets are defined:

USE(S) : the set of variables used in S
IN(S) : the set of variables that are live at the entry of S
OUT(S) : the set of variables that are live at the exit of S

Consider a basic block that consists of two statements, S1 followed by S2. Which one of the following statements is correct?

In the context of compilers, which of the following is/are NOT an intermediate representation of the source program?

Consider the following ANSI C program:

int main () {
    Integer x;
    return 0;
} 

Which one of the following phases in a seven-phase C compiler will throw an error?

Consider the following C code segment:

a = b + c;
e = a + 1;
d = b + c;
f = d + 1;
g = e + f;

In a compiler, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes in the DAG is _____________

Consider the following grammar (that admits a series of declarations, followed by expressions) and the associated syntax directed translation (SDT) actions, given as pseudo-code

\begin{array}{lll} P & \rightarrow & D^* E^* \\ D & \rightarrow & \textsf{int ID} \{ \text{record that } \textsf{ID.} \text{lexeme is of type} \textsf{ int\}} \\ D & \rightarrow & \textsf{bool ID} \{ \text{record that } \textsf{ID.} \text{lexeme is of type} \textsf{ bool\}} \\ E& \rightarrow & E_1 +E_2 \{ \text{check that } E_1. \text{type}=E_2. \text{type} = \textsf{int}; \text{set } E.\text{type }:= \textsf{int} \} \\ E & \rightarrow & !E_1 \{ \text{check that } E_1. \text{type} = \textsf{bool}; \text{ set } E.\text{type} := \textsf{bool} \} \\ E & \rightarrow & \textsf{ID} \{ \text{set } E. \text{type } := \textsf{int} \} \end{array}

With respect to the above grammar, which one of the following choices is correct?

Consider the following statements.

S1: Every SLR(1) grammar is unambiguous but there are certain unambiguous grammars that are not SLR(1).
S2: For any context-free grammar, there is a parser that takes at most O(n^3) time to parse a string of length n.

Which one of the following options is correct?