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
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
$$bab$$
3
GATE CSE 2000
MCQ (Single Correct Answer)
+2
-0.6
Consider the following decision problems:
$${P_1}$$ Does a given finite state machine accept a given string
$${P_2}$$ Does a given context free grammar generate an infinite number of stings.

Which of the following statements is true?

A
Both $${P_1}$$ and $${P_2}$$ are decidable
B
Neither $${P_1}$$ and $${P_2}$$ are decidable
C
Only $${P_1}$$ is decidable
D
Only $${P_2}$$ is decidable
4
GATE CSE 1999
MCQ (More than One Correct Answer)
+2
-0.6
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
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