GATE CSE 2019 | Push Down Automata and Context Free Language Question 13 | Theory of Computation

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GATE CSE 2019

MCQ (Single Correct Answer)

-0.67

Which one of the following languages over $\Sigma=\{a, b\}$ is NOT context-free?

$\left\{w w^R \mid w \in\{a, b\}^*\right\}$

$\left\{w a^n b^n w^R \mid w \in\{a, b\}^*, n \geq 0\right\}$

$\left\{w a^n w^R b^n \mid w \in\{a, b\}^*, n \geq 0\right\}$

$\left\{a^n b^i \mid i \in\{n, 3 n, 5 n\}, n \geq 0\right\}$

GATE CSE 2018

MCQ (Single Correct Answer)

-0.6

Consider the following languages:

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m + p = n + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m = n$$ and $$p=q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m = n = p$$ and $$p \ne q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|mn = p + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$

Which of the languages above are context-free?

$${\rm I}$$ and $${\rm IV}$$ only

$${\rm I}$$ and $${\rm II}$$ only

$${\rm II}$$ and $${\rm III}$$ only

$${\rm II}$$ and $${\rm IV}$$ only

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-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?

$$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ or $$\,\,\,\,$$$$n > \left. 0 \right\}$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ and $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$

$$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ and $$\,\,\,n > \left. 0 \right\}\,\,\,\,$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.$$ or $$\,\,\,\,n \ge \left. 0 \right\}$$

$$\left\{ {{a^m}{b^n}|m \ge 0\,\,\,\,} \right.$$ or $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.\,$$ and $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$

$$\left\{ {{a^m}{b^n}|m \ge 0\,\,\,\,} \right.$$ and $$\,\,\,n > \left. 0 \right\}\,\,\,\,$$ and $$\left\{ {{a^m}{b^n}|m > 0\,\,\,\,} \right.\,$$ or $$\,\,\,\,n > \left. 0 \right\}\,\,\,\,$$

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

Which of the following languages are context-free? $$$\eqalign{ & {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^m}{b^n}{a^m}{b^n}|m,n \ge 1} \right\} \cr & {L_3} = \left\{ {{a^m}{b^n}|m = 2n + 1} \right\} \cr} $$$

$${L_1}$$ and $${L_2}$$ only

$${L_1}$$ and $${L_3}$$ only

$${L_2}$$ and $${L_3}$$ only

$${L_3}$$ only

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