1
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
The language $$\left\{ {{a^m}{b^n}{c^{m + n}}\left| {m,n \ge } \right.} \right\}$$ is
A
Regular
B
Context-free but not regular
C
Context sensitive but not context free
D
Type-$$0$$ but not context sensitive
2
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
Consider the following grammar $$G:$$
$$\eqalign{ & S \to bS\,\left| {\,aA\,\left| {\,b} \right.} \right. \cr & A \to bA\,\left| {\,aB} \right. \cr & B \to bB\,\left| {\,aS\,\left| {\,a} \right.} \right. \cr} $$

Let $${N_a}\left( w \right)$$ and $${N_b}\left( w \right)$$ denote the number of $$a's$$ and $$b's$$ in a string $$w$$ respectively. The language
$$L\left( G \right)\,\,\, \subseteq \left\{ {a,b} \right\} + $$ generated by $$G$$ is

A
$$\left\{ {w\,\left| {Na\left( w \right) > 3Nb\left( w \right)} \right.} \right\}$$
B
$$\left\{ {w\,\left| {Nb\left( w \right) > 3Na\left( w \right)} \right.} \right\}$$
C
$$\left\{ {w\,\left| {Na\left( w \right) = 3k,k \in \left\{ {0,1,2,...} \right\}} \right.} \right\}$$
D
$$\left\{ {w\,\left| {Nb\left( w \right) = 3k,k \in \left\{ {0,1,2,...} \right\}} \right.} \right\}$$
3
GATE CSE 1999
MCQ (More than One Correct Answer)
+2
-0
If $${L_1}$$ is a context free language and $${L_2}$$ is a regular which of the following is/are false?
A
$${L_1} - {L_2}$$ is not context free
B
$${L_1} \cap {L_2}$$ is context free
C
$$ \sim {L_1}$$ is context free
D
$$ \sim {L_2}$$ is regular
4
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum state deterministic finite-state automation accepting $$L$$ is
A
$$2$$
B
$$5$$
C
$$8$$
D
$$3$$
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