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All questions of Regular & Context Free Languages, Pumping Lemma for Computer Science Engineering (CSE) Exam
Let w= xyz and y refers to the middle portion and |y|>0.What do we call the process of repeating y 0 or more times before checking that they still belong to the language L or not?- a)Generating
- b)Pumping
- c)Producing
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Let w= xyz and y refers to the middle portion and |y|>0.What do we call the process of repeating y 0 or more times before checking that they still belong to the language L or not?
a)
Generating
b)
Pumping
c)
Producing
d)
None of the mentioned
|
Subhankar Chawla answered |
Refers to the absolute value of y.
Answer in accordance to the third and last statement in pumping lemma:
For all _______ xyiz ∈L- a)i>0
- b)i<0
- c)i<=0
- d)i>=0
Correct answer is option 'D'. Can you explain this answer?
Answer in accordance to the third and last statement in pumping lemma:
For all _______ xyiz ∈L
For all _______ xyiz ∈L
a)
i>0
b)
i<0
c)
i<=0
d)
i>=0
|
Saranya Banerjee answered |
For all strings xyiz in the language L, where |xy| ≤ p and |y| > 0, there exists a string w ∈ L such that w can be written as xy^iz.
While applying Pumping lemma over a language, we consider a string w that belong to L and fragment it into _________ parts.- a)2
- b)5
- c)3
- d)6
Correct answer is option 'C'. Can you explain this answer?
While applying Pumping lemma over a language, we consider a string w that belong to L and fragment it into _________ parts.
a)
2
b)
5
c)
3
d)
6
|
Dishani Basu answered |
Pumping Lemma and Fragmenting the String
The Pumping Lemma is a powerful tool used in formal language theory to prove that certain languages are not regular. It provides a way to show that a language does not satisfy the conditions of regularity by considering the possible divisions of a string into parts.
The Steps:
To apply the Pumping Lemma, we need to follow these steps:
1. Assume L is a regular language.
2. Select a "pumping length" p for L.
3. Choose a string w that belongs to L and has a length of at least p.
4. Divide the string w into parts: uvxyz.
5. Consider the possible cases for the division of the string w:
- The string can be divided into 3 parts: uvxyz.
- The string can be divided into 5 parts: uvwxy.
- The string can be divided into 2 parts: xy.
- The string can be divided into 6 parts: uvwxyz.
- And so on...
Fragmenting the String:
In this specific question, we are considering a string w that belongs to the language L. The question asks us to fragment the string into a specific number of parts. The correct answer is option 'C', which means we need to fragment the string into 3 parts.
By fragmenting the string into 3 parts, we can analyze and manipulate the substrings u, v, x, and y to demonstrate that the language L does not satisfy the conditions of regularity. This is the essence of the Pumping Lemma, where we can show that no matter how we manipulate the substrings, we will eventually reach a point where the resulting string is not in the language L.
Therefore, by considering a string w that belongs to L and fragmenting it into 3 parts, we can effectively apply the Pumping Lemma to prove that the language L is not regular.
The Pumping Lemma is a powerful tool used in formal language theory to prove that certain languages are not regular. It provides a way to show that a language does not satisfy the conditions of regularity by considering the possible divisions of a string into parts.
The Steps:
To apply the Pumping Lemma, we need to follow these steps:
1. Assume L is a regular language.
2. Select a "pumping length" p for L.
3. Choose a string w that belongs to L and has a length of at least p.
4. Divide the string w into parts: uvxyz.
5. Consider the possible cases for the division of the string w:
- The string can be divided into 3 parts: uvxyz.
- The string can be divided into 5 parts: uvwxy.
- The string can be divided into 2 parts: xy.
- The string can be divided into 6 parts: uvwxyz.
- And so on...
Fragmenting the String:
In this specific question, we are considering a string w that belongs to the language L. The question asks us to fragment the string into a specific number of parts. The correct answer is option 'C', which means we need to fragment the string into 3 parts.
By fragmenting the string into 3 parts, we can analyze and manipulate the substrings u, v, x, and y to demonstrate that the language L does not satisfy the conditions of regularity. This is the essence of the Pumping Lemma, where we can show that no matter how we manipulate the substrings, we will eventually reach a point where the resulting string is not in the language L.
Therefore, by considering a string w that belongs to L and fragmenting it into 3 parts, we can effectively apply the Pumping Lemma to prove that the language L is not regular.
Fill in the blank in terms of p, where p is the maximum string length in L.
Statement: Finite languages trivially satisfy the pumping lemma by having n = ______- a)p*1
- b)p+1
- c)p-1
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Fill in the blank in terms of p, where p is the maximum string length in L.
Statement: Finite languages trivially satisfy the pumping lemma by having n = ______
Statement: Finite languages trivially satisfy the pumping lemma by having n = ______
a)
p*1
b)
p+1
c)
p-1
d)
None of the mentioned
|
Sudhir Patel answered |
Finite languages trivially satisfy the pumping lemma by having n equal to the maximum string length in l plus 1.
If we select a string w such that w∈L, and w=xyz. Which of the following portions cannot be an empty string?- a)x
- b)y
- c)z
- d)all of the mentioned
Correct answer is option 'B'. Can you explain this answer?
If we select a string w such that w∈L, and w=xyz. Which of the following portions cannot be an empty string?
a)
x
b)
y
c)
z
d)
all of the mentioned
|
|
Sudhir Patel answered |
The lemma says, the portion y in xyz cannot be zero or empty i.e. |y|>0, this condition needs to be fulfilled to check the conclusion condition.
Which of the following one can relate to the given statement:
Statement: If n items are put into m containers, with n>m, then atleast one container must contain more than one item.- a)Pumping lemma
- b)Pigeon Hole principle
- c)Count principle
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Which of the following one can relate to the given statement:
Statement: If n items are put into m containers, with n>m, then atleast one container must contain more than one item.
Statement: If n items are put into m containers, with n>m, then atleast one container must contain more than one item.
a)
Pumping lemma
b)
Pigeon Hole principle
c)
Count principle
d)
None of the mentioned
|
|
Raghav Sharma answered |
The options for the statement are missing. Could you please provide the options for me to choose from?
Relate the following statement:
Statement: All sufficiently long words in a regular language can have a middle section of words repeated a number of times to produce a new word which also lies within the same language.- a)Turing Machine
- b)Pumping Lemma
- c)Arden’s theorem
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Relate the following statement:
Statement: All sufficiently long words in a regular language can have a middle section of words repeated a number of times to produce a new word which also lies within the same language.
Statement: All sufficiently long words in a regular language can have a middle section of words repeated a number of times to produce a new word which also lies within the same language.
a)
Turing Machine
b)
Pumping Lemma
c)
Arden’s theorem
d)
None of the mentioned
|
|
Sudhir Patel answered |
Pumping lemma defines an essential property for every regular language in automata theory. It has certain rules which decide whether a language is regular or not.
Let w be a string and fragmented by three variable x, y, and z as per pumping lemma. What does these variables represent?- a)string count
- b)string
- c)string count and string
- d)none of the mentioned
Correct answer is option 'A'. Can you explain this answer?
Let w be a string and fragmented by three variable x, y, and z as per pumping lemma. What does these variables represent?
a)
string count
b)
string
c)
string count and string
d)
none of the mentioned
|
|
Sudhir Patel answered |
Given: w =xyz. Here, xyz individually represents strings or rather substrings which we compute over conditions to check the regularity of the language.
There exists a language L. We define a string w such that w∈L and w=xyz and |w| >=n for some constant integer n.What can be the maximum length of the substring xy i.e. |xy|<=?- a)n
- b)|y|
- c)|x|
- d)none of the mentioned
Correct answer is option 'A'. Can you explain this answer?
There exists a language L. We define a string w such that w∈L and w=xyz and |w| >=n for some constant integer n.What can be the maximum length of the substring xy i.e. |xy|<=?
a)
n
b)
|y|
c)
|x|
d)
none of the mentioned
|
|
Sudhir Patel answered |
It is the first conditional statement of the lemma that states that |xy|<=n, i.e. the maximum length of the substring xy in w can be n only.
If d is a final state, which of the following is correct according to the given diagram?
- a)x=p, y=qr, z=s
- b)x=p, z=qrs
- c)x=pr, y=r, z=s
- d)All of the mentioned
Correct answer is option 'A'. Can you explain this answer?
If d is a final state, which of the following is correct according to the given diagram?
a)
x=p, y=qr, z=s
b)
x=p, z=qrs
c)
x=pr, y=r, z=s
d)
All of the mentioned
|
|
Sudhir Patel answered |
The FSA accepts the string pqrs. In terms of pumping lemma, the string pqrs is broken into an x portion an a, a y portion qr and a z portion s.
Chapter doubts & questions for Regular & Context Free Languages, Pumping Lemma - Theory of Computation 2025 is part of Computer Science Engineering (CSE) exam preparation. The chapters have been prepared according to the Computer Science Engineering (CSE) exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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