GATE CSE 2019 | Finite Automata and Regular Language Question 21 | Theory of Computation

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GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

If L is a regular language over Σ = {a,b}, which one of the following languages is NOT regular?

Suffix (L) = {y ∈ Σ* such that xy ∈ L}

{ww^R │w ∈ L}

Prefix (L) = {x ∈ Σ*│∃y ∈ Σ* such that xy ∈ L}

L ∙ L^R = {xy │ x ∈ L, y^R ∈ L}

GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

For Σ = {a, b}, let us consider the regular language L = {x | x = a^2+3k or x = b^10+12k, k ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $$0s$$ and two consecutive $$1s?$$

$$\left( {0 + 1} \right){}^ * 0011\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 1100\left( {0 + 1} \right){}^ * $$

$$\left( {0 + 1} \right){}^ * \left( {00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * \left. {00} \right)} \right.\left( {0 + 1} \right){}^ * $$

$$\left( {0 + 1} \right){}^ * 00\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 11\left( {0 + 1} \right){}^ * $$

$$00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * 00$$

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

-0.3

Language $${L_1}$$ is defined by the grammar: $$S{}_1 \to a{S_1}b|\varepsilon $$
Language $${L_2}$$ is defined by the grammar: $$S{}_2 \to ab{S_2}|\varepsilon $$

Consider the following statements:
$$P:$$ $${L_1}$$ is regular
$$Q:$$ $${L_2}$$ is regular

Which one of the following is TRUE?

Both $$P$$ and $$Q$$ are true

$$P$$ is true and $$Q$$ is false

$$P$$ is false and $$Q$$ is true

Both $$P$$ and $$Q$$ are false

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