1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6

Which one of the following grammars generates the following language?

$$L = \left( {{a^i}{b^j}|i \ne j} \right)$$
A
$$\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\,a\,|\,b \cr & A \to aA\,|\, \in \cr & B \to Bb\,|\, \in \cr} $$
B
$$S \to aS\,|\,Sb\,|\,a\,|\,b$$
C
$$\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\, \in \cr & A \to aA\,|\, \in \cr & B \to Bb\,|\, \in \cr} $$
D
$$\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\, \in \cr & A \to aA\,|\,a \cr & B \to Bb\,|\,b \cr} $$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
In the correct grammar of the previous question, what is the length of the derivation (number of steps starring from S) to generate the string $${a^l}{b^m}$$ with $$l \ne m$$?
A
$$\max (l,m) + 2$$
B
$$l + m + 2$$
C
$$l + m + 3$$
D
$$\max (l,m) + 3$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6

Consider the following grammar:

$$\eqalign{ & S \to FR \cr & R \to *S\,|\,\varepsilon \cr & F \to id \cr} $$

In the predictive parser table, M, of the grammar the entries $$M\left[ {S,id} \right]$$ and $$M\left[ {R,\$ } \right]$$ respectively.

A
$$\left\{ {S \to FR} \right\}$$ and $$\left\{ {R \to \varepsilon } \right\}$$
B
$$\left\{ {S \to FR} \right\}$$ and $$\left\{ {\,\,} \right\}$$
C
$$\left\{ {S \to FR} \right\}$$ and $$\left\{ {R \to * S} \right\}$$
D
$$\left\{ {F \to id} \right\}$$ and $$\left\{ {R \to \varepsilon } \right\}$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6

Consider the following translation scheme.

$$\eqalign{ & S \to ER \cr & R \to *E\left\{ {pr{\mathop{\rm int}} ('*');} \right\}R\,|\,\varepsilon \cr & E \to F + E\left\{ {pr{\mathop{\rm int}} (' + ');} \right\}\,|\,F \cr & F \to S\,|\,id\,\left\{ {pr{\mathop{\rm int}} (id.value);} \right\} \cr} $$

Here id is a token that represents an integer and id.value represents the corresponding integer value. For an input '2 * 3 + 4' this translation scheme prints

A
2 * 3 + 4
B
2 * + 3 4
C
2 3 * 4 +
D
2 3 4 + *
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