1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the language :
$${L_1} = \left\{ {{a^n}{b^n}{c^m}\left| {n,m > 0} \right.} \right\}$$ and $${L_2} = \left\{ {{a^n}{b^m}{c^m}\left| {n,m > 0} \right.} \right\}$$

Which of the following statement is FALSE?

A
$${L_1}\, \cap \,{L_2}$$ is a context-free language
B
$${L_1}\, \cap \,{L_2}$$ is a context-free language
C
$${L_1}$$ and $${L_2}$$ are context-free language
D
$${L_1}\, \cap \,{L_2}$$ is a context sensitive language
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the language :
$${L_1}\, = \left\{ {w\,{w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$
$${L_2}\, = \left\{ {w\, \ne {w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$ where $$ \ne $$ is a special symbol
$${L_3}\, = \left\{ {w\,w\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$

Which one of the following is TRUE?

A
$${L_1}$$ $$=$$ is a deterministic $$CFL$$
B
$${L_2}$$ $$=$$ is a deterministic $$CFL$$
C
$${L_3}$$ is a $$CFL,$$ but not a deterministic $$CFL$$
D
$${L_3}$$ IS A DETERMINISTIC $$CFL$$
3
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
Let $$M = \left( {K,\,\sum {,\,F,\,\Delta ,\,s,\,F} } \right)$$ be a pushdown automation. Where $$K = \left\{ {s,\,f} \right\},\,F = \left\{ f \right\},\,\sum { = \left\{ {a,b} \right\},\,F = \left\{ a \right\}} $$ and $$\Delta = \left\{ {\left( {\left( {s,\,a,\, \in } \right)} \right.,\,\left. {\left( {s,\,a} \right)} \right),\,\left( {\left( {s,\,b,\, \in } \right),\,\left. {\left( {s,\,a} \right)} \right),\,} \right.} \right.$$ $$\left( {\left( {s,\,a,\, \in } \right),\,\left( {f,\, \in } \right),\,\left( {\left( {f,\,a,\,a} \right),\,\left. {\left( {f,\, \in } \right)} \right),\,\left( {\left( {f,\,b,\,a} \right),\,\left. {\left. {\left( {f,\, \in } \right)} \right)} \right\}} \right.} \right.} \right..$$

Which one of the following strings is not a number of $$L(M)?$$

A
$$aaa$$
B
$$aabab$$
C
$$baaba$$
D
$$bab$$
4
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
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