1
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
The cube root of a natural number n is defined as the largest natural number m such that $${m^3} \le n$$. The complexity of computing the cube root of n (n is represented in binary notation) is
A
O(n) but not O(n0.5)
B
O(n0.5) but not O((log n)k) for any constant k > 0
C
O((log n)k) for some constant k > 0, but not O((log log n)m) for any constant m > 0
D
O((log log n)k) for some constant k > 0.5, but not O((log log n)0.5)
2
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6

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

A
$$\{ \,S' \to eS\,\} $$ and $$\{ \,S' \to \varepsilon \,\} $$
B
$$\{ \,S' \to eS\,\} $$ and $$\{ \,\,\,\} $$
C
$$\{ \,S' \to \varepsilon \,\} $$ and $$\{ \,S' \to \varepsilon \,\} $$
D
$$\{ \,S' \to eS\,,S' \to \varepsilon \} $$ and $$\{ \,S' \to \varepsilon \,\} $$
3
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?
A
Removing left recursion alone
B
Factoring the grammar alone
C
Removing left recursion and factoring the grammar
D
None of the above
4
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
In a bottom-up evaluation of a syntax directed definition, inherited attributes can
A
always be evaluated
B
be evaluated only if the definition is L- attributed
C
be evaluated only if the definition has synthesized attributes
D
never be evaluated
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