GATE CSE 2014 Set 1 | Finite Automata and Regular Language Question 47 | Theory of Computation

GATE CSE 2014 Set 1

MCQ (Single Correct Answer)

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Consider the finite automation in the following figure. GATE CSE 2014 Set 1 Theory of Computation - Finite Automata and Regular Language Question 90 English

GATE CSE 2014 Set 1 Theory of Computation - Finite Automata and Regular Language Question 90 English

What is the set of reachable states for the input string $$0011?$$

$$\left\{ {{q_0},\,{q_1},\,{q_2}} \right\}$$

$$\left\{ {{q_0},\,{q_1}} \right\}$$

$$\left\{ {{q_0},\,{q_1},\,{q_2},\,{q_3}} \right\}$$

$$\left\{ {{q_3}} \right\}$$

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

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If $${L_1} = \left\{ {{a^n}\left| {n \ge \left. 0 \right\}} \right.} \right.$$ and $${L_2} = \left\{ {{b^n}\left| {n \ge \left. 0 \right\}} \right.} \right.,$$ consider
$$\left. {\rm I} \right)$$ $$\,\,\,{L_{1 \bullet }}{L_2}$$ is a regular language
$$\left. {\rm II} \right)$$ $$\,\,\,{L_{1 \bullet }}{L_2} = \left\{ {{a^n}{b^n}\left| {n \ge \left. 0 \right\}} \right.} \right.$$
Which one of the following is CORRECT?

Only $$\left( {\rm I} \right)$$

Only $$\left( {\rm II} \right)$$

Both $$\left( {\rm I} \right)$$ and $$\left( {\rm II} \right)$$

Neither $$\left( {\rm I} \right)$$ nor $$\left( {\rm II} \right)$$

GATE CSE 2013

MCQ (Single Correct Answer)

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Consider the languages $${L_1} = \phi $$ and $${L_2} = \left\{ a \right\}.$$ Which one of the following represents $${L_1}\,L_2^ * UL_1^ * ?$$

$$\left\{ \varepsilon \right\}$$

$$\phi $$

$${a^ * }$$

$$\left\{ {\varepsilon ,a} \right\}$$

GATE CSE 2012

MCQ (Single Correct Answer)

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What is the complement of the language accepted by the $$NFA$$ shown below?
Assume $$\sum { = \left\{ a \right\}\,\,} $$ and $$\varepsilon $$ is the empty string. GATE CSE 2012 Theory of Computation - Finite Automata and Regular Language Question 93 English