Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:

diam(G) = $$\displaystyle\max_{u, x\in V}$$ {the length of shortest path between u and v}

Let M be the adjacency matrix of G.

Define graph G₂ on the same set of vertices with adjacency matrix N, where

$$N_{ij} =\left\{ {\begin{array}{*{20}{c}} {1 \ \ \text{if} \ \ {M_{ij}} > 0 \ \ \text{or} \ \ P_{ij} > 0, \ \text{where} \ \ P = {M^2}}\\ {0, \ \ \ \ \ \text{otherwise}} \end{array}} \right.$$

Which one of the following statements is true?

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(n³) time to parse a string of length n.

Which one of the following option is correct?

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:

P → D* E*

D → int ID {record that ID.lexeme is of type int}

D → bool ID { record that ID.lexeme is of type bool}

E → E₁ + E₂ {check that E₁.type = E₂.type = int; set E.type := int}

E → !E₁ {check that E₁.type = bool; set E.type := bool}

E → ID {set E.type := int}

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

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 of nodes in the DAG is ______