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1

GATE CSE 2007

MCQ (Single Correct Answer)
Consider the following two statements:

P: Every regular grammar is LL(1)
Q: Every regular set has a LR(1) grammar

Which of the following is TRUE?
A
Both P and Q are true
B
P is true and Q is false
C
P is false and Q is true
D
Both P and Q are false
2

GATE CSE 2006

MCQ (Single Correct Answer)

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 $$\left\{ {R \to \varepsilon } \right\}$$
3

GATE CSE 2006

MCQ (Single Correct Answer)
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
$$\max (l,m) + 3$$
4

GATE CSE 2006

MCQ (Single Correct Answer)

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
$$\eqalign{ & S \to AC\,|\,CB \cr & C \to aCb\,|\, \in \cr & A \to aA\,|\,a \cr & B \to Bb\,|\,b \cr} $$

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