1
GATE CSE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the following context-free grammars:
$$\eqalign{ & {G_1}:\,\,\,\,\,S \to aS|B,\,\,B \to b|bB \cr & {G_2}:\,\,\,\,\,S \to aA|bB,\,\,A \to aA|B|\varepsilon ,\,\,B \to bB|\varepsilon \cr} $$

Which one of the following pairs of languages is generated by $${G_1}$$ and $${G_2}$$, respectively?

A
$$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ or $$\,\,\,\,$$$$n > \left. 0 \right\}$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ and $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$
B
$$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ and $$\,\,\,n > \left. 0 \right\}\,\,\,\,$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ or $$\,\,\,\,n \ge \left. 0 \right\}$$
C
$$\left\{ {{a^m}{b^n}|m \ge 0\,\,\,\,} \right.$$ or $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.\,$$ and $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$
D
$$\left\{ {{a^m}{b^n}|m \ge 0\,\,\,\,} \right.$$ and $$\,\,\,n > \left. 0 \right\}\,\,\,\,$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.\,$$ or $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Which of the following languages are context-free? $$$\eqalign{ & {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^m}{b^n}{a^m}{b^n}|m,n \ge 1} \right\} \cr & {L_3} = \left\{ {{a^m}{b^n}|m = 2n + 1} \right\} \cr} $$$
A
$${L_1}$$ and $${L_2}$$ only
B
$${L_1}$$ and $${L_3}$$ only
C
$${L_2}$$ and $${L_3}$$ only
D
$${L_3}$$ only
3
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider the following languages over the alphabet $$\sum { = \left\{ {0,\,1,\,c} \right\}:} $$
$$\eqalign{ & {L_1} = \left\{ {{0^n}\,{1^n}\,\left| {n \ge } \right.0} \right\} \cr & {L_2} = \left\{ {wc{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr & {L_3} = \left\{ {w{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr} $$

Here, $${w^r}$$ is the reverse of the string $$w.$$ Which of these languages are deterministic Context- free languages?

A
None of the languages
B
$$(B)$$ Only $${L_1}$$
C
Only $${L_1}$$ and $${L_2}$$
D
All the three languages.
4
GATE CSE 2013
MCQ (Single Correct Answer)
+2
-0.6
Consider the $$DFA$$ $$A$$ given below. GATE CSE 2013 Theory of Computation - Push Down Automata and Context Free Language Question 20 English

Which of the following are FALSE?
$$1.$$ Complement of $$L(A)$$ is context - free.
$$2.$$ $$L(A)$$ $$ = \left( {{{11}^ * }0 + 0} \right)\left( {0 + 1} \right){}^ * {0^ * }\left. {{1^ * }} \right)$$
$$3.$$ For the language accepted by $$A, A$$ is the minimal $$DFA.$$
$$4.$$ $$A$$ accepts all strings over $$\left\{ {0,1} \right\}$$ of length at least $$2.$$

A
$$1$$ and $$3$$ only
B
$$2$$ and $$4$$ only
C
$$2$$ and $$3$$ only
D
$$3$$ and $$4$$ only
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