GATE CSE 2014 Set 2 | Finite Automata and Regular Language Question 45 | Theory of Computation

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?

$${L_1}$$ is regular but not $${L_2}$$

$${L_2}$$ is regular but not $${L_1}$$

Both $${L_1}$$ and $${L_2}$$ are regular

Neither $${L_1}$$ nor $${L_2}$$ are regular

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

$${L_1}$$ is regular but not $${L_2}$$

$${L_2}$$ is regular but not $${L_1}$$

Both $${L_1}$$ and $${L_2}$$ are regular

Neither $${L_1}$$ nor $${L_2}$$ are regular

GATE CSE 2014 Set 1

MCQ (Single Correct Answer)

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Which of the regular expression given below represent the following $$DFA?$$ GATE CSE 2014 Set 1 Theory of Computation - Finite Automata and Regular Language Question 55 English 1

GATE CSE 2014 Set 1 Theory of Computation - Finite Automata and Regular Language Question 55 English 1

GATE CSE 2014 Set 1 Theory of Computation - Finite Automata and Regular Language Question 55 English 2

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

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

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

$${\rm I}$$, $${\rm II}$$ and $${\rm III}$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.6

Consider the following languages
$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

Which one of the following statements is FALSE?

$${L_2}$$ is context-free

$${L_1} \cap {L_2}$$ is context-free

Complement of $${L_2}$$ is recursive

Complement of $${L_1}$$ is context-free but not regular

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