1

GATE CSE 2006

MCQ (Single Correct Answer)

+2

-0.6

Consider the following statements about the context-free grammar

$$G = \left\{ {S \to SS,\,S \to ab,\,S \to ba,\,S \to \varepsilon } \right\}$$

$$1.$$ $$G$$ is ambiguous

$$2.$$ $$G$$ produces all strings with equal number of $$a's$$ and $$b's$$

$$3.$$ $$G$$ can be accepted by a deterministic $$PDA$$.

$$G = \left\{ {S \to SS,\,S \to ab,\,S \to ba,\,S \to \varepsilon } \right\}$$

$$1.$$ $$G$$ is ambiguous

$$2.$$ $$G$$ produces all strings with equal number of $$a's$$ and $$b's$$

$$3.$$ $$G$$ can be accepted by a deterministic $$PDA$$.

Which combination below expresses all the true statements about $$G?$$

2

GATE CSE 2005

MCQ (Single Correct Answer)

+2

-0.6

Let $${N_f}$$ and $${N_p}$$ denote the classes of languages accepted by non-deterministic finite automata and non-deterministic push-down automata, respectively. Let $${D_f}$$ and $${D_p}$$ denote the classes of languages accepted by deterministic finite automata and deterministic push-down automata, respectively. Which one of the following is TRUE?

3

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 $${L_2} = \left\{ {{a^n}{b^m}{c^m}\left| {n,m > 0} \right.} \right\}$$

$${L_1} = \left\{ {{a^n}{b^n}{c^m}\left| {n,m > 0} \right.} \right\}$$ and $${L_2} = \left\{ {{a^n}{b^m}{c^m}\left| {n,m > 0} \right.} \right\}$$

Which of the following statement is FALSE?

4

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

$${L_3}\, = \left\{ {w\,w\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$

$${L_1}\, = \left\{ {w\,{w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$

$${L_2}\, = \left\{ {w\, \ne {w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$ 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?

Questions Asked from Push Down Automata and Context Free Language (Marks 2)

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