1
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
Consider the languages $${L_1}$$, $${L_2}$$ and $${L_3}$$ are given below. $$$\eqalign{ & {L_1} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.} \right\} \cr & {L_2} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.\,\,and\,\,p = q} \right\}\,\,and \cr & {L_3} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r\, \in N\,\,\,and\,\,\,p = q = r} \right.} \right\}. \cr} $$$

Which of the following statements is not TRUE?

A
Pushdown automata $$(PDA)$$ can be used to recognize $${L_1}$$ and $${L_2}$$
B
$${L_1}$$ is a regular language
C
All the three languages are context free
D
Turing machines can be used to recognize all the languages
2
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
A deterministic finite automation $$(DFA)$$ $$D$$ with alphabet $$\sum { = \left\{ {a,b} \right\}} $$ is given below GATE CSE 2011 Theory of Computation - Push Down Automata and Context Free Language Question 23 English

Which of the following finite state machines is a valid minimal $$DFA$$ which accepts the same languages as $$D?$$

A
GATE CSE 2011 Theory of Computation - Push Down Automata and Context Free Language Question 23 English Option 1
B
GATE CSE 2011 Theory of Computation - Push Down Automata and Context Free Language Question 23 English Option 2
C
GATE CSE 2011 Theory of Computation - Push Down Automata and Context Free Language Question 23 English Option 3
D
GATE CSE 2011 Theory of Computation - Push Down Automata and Context Free Language Question 23 English Option 4
3
GATE CSE 2010
MCQ (Single Correct Answer)
+2
-0.6
Consider the languages $$$\eqalign{ & {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr & {L_3} = \left\{ {{0^i}{1^j}\,\left| {i = 2j + 1} \right.} \right\}, \cr & {L_4} = \left\{ {{0^i}{1^j}\,\left| {i \ne 2j} \right.} \right\}, \cr} $$$
A
only $${L_2}$$ is context free
B
only $${L_2}$$ and $${L_3}$$ are context free
C
only $${L_1}$$ and $${L_2}$$ are context free
D
all are context free
4
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
Which of the following statement is false?
A
Every $$NFA$$ can be converted to an equivalent $$DFA$$
B
Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine.
C
Every regular language is also a context- free language
D
Every subset of a recursively enumerable set is recursive
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