Pumping Lemma for regular languages MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: September 23, 2024

MCQs on Properties of Regular Languages
Which of the following is a property of regular languages?

A) Closed under intersection
B) Closed under complement
C) Closed under union
D) All of the above
Answer: D) All of the above

Which of the following operations cannot be performed on regular languages and still produce a regular language?

A) Union
B) Intersection
C) Complement
D) None of the above
Answer: D) None of the above

Which of the following statements about regular languages is false?

A) Every finite language is regular.
B) The concatenation of two regular languages is regular.
C) The set of all regular languages is closed under difference.
D) The set of all regular languages is closed under homomorphism.
Answer: C) The set of all regular languages is closed under difference.

If
𝐿
L is a regular language, which of the following is also guaranteed to be regular?

A) The reversal of
𝐿
L
B) The intersection of
𝐿
L with a context-free language
C) The set of prefixes of strings in
𝐿
L
D) The set of suffixes of strings in
𝐿
L
Answer: A) The reversal of
𝐿
L

Which of the following is a decidable property of regular languages?

A) Emptiness
B) Finiteness
C) Membership
D) All of the above
Answer: D) All of the above

Which of the following closure properties does not hold for regular languages?

A) Closure under symmetric difference
B) Closure under inverse homomorphism
C) Closure under Kleene star
D) Closure under intersection with a context-free language
Answer: D) Closure under intersection with a context-free language

What does the Pumping Lemma for regular languages state?

A) If a language is regular, then there exists a constant such that any string longer than this constant can be divided into three parts satisfying certain conditions.
B) If a language is regular, it must contain an infinite number of strings.
C) If a language is regular, it must be accepted by some DFA.
D) If a language is regular, it can be represented by a regular expression.
Answer: A) If a language is regular, then there exists a constant such that any string longer than this constant can be divided into three parts satisfying certain conditions.

Which of the following statements is true for regular languages?

A) Regular languages are closed under union, but not under intersection.
B) Regular languages are closed under both union and intersection.
C) Regular languages are closed under union, but not under complementation.
D) Regular languages are closed under neither union nor intersection.
Answer: B) Regular languages are closed under both union and intersection.

Which of the following is not a property of regular languages?

A) Closed under shuffle
B) Closed under quotient with regular languages
C) Closed under reversal
D) Closed under homomorphism
Answer: A) Closed under shuffle

If
𝐿
L is a regular language, which of the following is not necessarily regular?

A) The complement of
𝐿
L
B) The union of
𝐿
L with another regular language
C) The intersection of
𝐿
L with a context-free language
D) The set of all strings not in
𝐿
L
Answer: C) The intersection of
𝐿
L with a context-free language

These questions cover various properties of regular languages, including closure properties, decidability, and the implications of the Pumping Lemma.

 

 

Pumping Lemma for regular languages MCQs write on mcqs with answer
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Here are some multiple-choice questions (MCQs) on the Pumping Lemma for regular languages, along with their answers:

MCQs on Pumping Lemma for Regular Languages
What does the Pumping Lemma for regular languages primarily prove?

A) That all languages are regular.
B) That certain languages are not regular.
C) That all regular languages are finite.
D) That regular languages are closed under intersection.
Answer: B) That certain languages are not regular.

Which of the following conditions must hold for a string
𝑠
s in a regular language according to the Pumping Lemma?

A)
𝑠
s can be divided into three parts
𝑥
,
𝑦
,
𝑧
x,y,z such that
𝑠
=
𝑥
𝑦
𝑧
s=xyz,
∣
𝑥
𝑦
∣
≤
𝑝
∣xy∣≤p, and
∣
𝑦
∣
>
0
∣y∣>0.
B)
𝑠
s can be divided into three parts
𝑥
,
𝑦
,
𝑧
x,y,z such that
𝑠
=
𝑥
𝑦
𝑧
s=xyz,
∣
𝑥
𝑦
∣
>
𝑝
∣xy∣>p, and
∣
𝑦
∣
≥
0
∣y∣≥0.
C)
𝑠
s can be divided into three parts
𝑥
,
𝑦
,
𝑧
x,y,z such that
𝑠
=
𝑥
𝑦
𝑧
s=xyz,
∣
𝑥
∣
=
𝑝
∣x∣=p, and
∣
𝑦
∣
≥
0
∣y∣≥0.
D)
𝑠
s can be divided into three parts
𝑥
,
𝑦
,
𝑧
x,y,z such that
𝑠
=
𝑥
𝑦
𝑧
s=xyz,
∣
𝑥
𝑦
𝑧
∣
=
𝑝
∣xyz∣=p, and
∣
𝑦
∣
=
0
∣y∣=0.
Answer: A)
𝑠
s can be divided into three parts
𝑥
,
𝑦
,
𝑧
x,y,z such that
𝑠
=
𝑥
𝑦
𝑧
s=xyz,
∣
𝑥
𝑦
∣
≤
𝑝
∣xy∣≤p, and
∣
𝑦
∣
>
0
∣y∣>0.

Which of the following is NOT a requirement for the Pumping Lemma?

A) The language must be infinite.
B) The string
𝑠
s must be long enough (length at least
𝑝
p).
C) The part
𝑦
y can be pumped (repeated) any number of times, including zero.
D) The part
𝑥
x can be pumped (repeated) any number of times, including zero.
Answer: D) The part
𝑥
x can be pumped (repeated) any number of times, including zero.

In the context of the Pumping Lemma, what is
𝑝
p?

A) The length of the shortest string in the language.
B) The pumping length, a constant depending on the language.
C) The number of states in the minimal DFA for the language.
D) The number of states in the minimal NFA for the language.
Answer: B) The pumping length, a constant depending on the language.

Which of the following languages can be shown to be non-regular using the Pumping Lemma?

A)
{
𝑎
𝑛
𝑏
𝑛
∣
𝑛
≥
0
}
{a
n
b
n
∣n≥0}
B)
{
𝑎
𝑛
𝑏
𝑚
∣
𝑛
,
𝑚
≥
0
}
{a
n
b
m
∣n,m≥0}
C)
{
𝑎
∗
𝑏
∗
}
{a
∗
b
∗
}
D)
{
𝑎
𝑛
∣
𝑛
≥
0
}
{a
n
∣n≥0}
Answer: A)
{
𝑎
𝑛
𝑏
𝑛
∣
𝑛
≥
0
}
{a
n
b
n
∣n≥0}

True or False: If a language satisfies the Pumping Lemma, it is necessarily regular.

A) True
B) False
Answer: B) False

In the Pumping Lemma, if a string
𝑠
=
𝑥
𝑦
𝑧
s=xyz can be pumped, which of the following must be true?

A) For every
𝑖
≥
0
i≥0,
𝑥
𝑦
𝑖
𝑧
xy
i
z is in the language.
B) For some
𝑖
≥
0
i≥0,
𝑥
𝑦
𝑖
𝑧
xy
i
z is in the language.
C) For every
𝑖
>
0
i>0,
𝑥
𝑦
𝑖
𝑧
xy
i
z is in the language.
D) For
𝑖
=
0
i=0,
𝑥
𝑦
𝑖
𝑧
xy
i
z is not in the language.
Answer: A) For every
𝑖
≥
0
i≥0,
𝑥
𝑦
𝑖
𝑧
xy
i
z is in the language.

Which of the following is a common use of the Pumping Lemma?

A) To show that a language is regular.
B) To convert a DFA to an NFA.
C) To show that a language is not regular.
D) To minimize the number of states in a DFA.
Answer: C) To show that a language is not regular.

According to the Pumping Lemma, what can be said about the substring
𝑦
y in
𝑠
=
𝑥
𝑦
𝑧
s=xyz?

A) It can be empty.
B) It cannot be empty.
C) It must be longer than
𝑧
z.
D) It must be longer than
𝑥
x.
Answer: B) It cannot be empty.

Which of the following statements about the Pumping Lemma is correct?

A) If a language fails the Pumping Lemma, it must be regular.
B) If a language satisfies the Pumping Lemma, it must be regular.
C) If a language satisfies the Pumping Lemma, it might be regular or non-regular.
D) If a language fails the Pumping Lemma, it might be regular or non-regular.
Answer: C) If a language satisfies the Pumping Lemma, it might be regular or non-regular.

 

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