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Questions tagged [pumping-lemma]

A lemma mostly used to prove that a language is not regular/context-free.

From wikipedia,

In the theory of formal languages in computability theory, a pumping lemma or pumping argument states that, for a particular language to be a member of a language class, any sufficiently long string in the language contains a section, or sections, that can be removed, or repeated any number of times, with the resulting string remaining in that language. The proofs of these lemmas typically require counting arguments such as the pigeonhole principle.

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Regular language?

I have a compiler question. Determine whether {(ab)^n | n >= 0} is a regular language? But I can draw its NFA. But if I use pumping lemma, I will get a contradiction answer. Can anyone help me ?
cihm
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Pumping Lemma for regular language: Can we modify the first condition to 'for each i > 0'?

Pumping lemma from " Question: Can we modify the first condition to for each i > 0 instead of for each i ≥ 0 ?
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Prove language is not context-free using pumping lemma

I have the following alphabet: Σ = {0, 1, . . . , 9} and the Language L defined as: L = { abc | a + b = c} where substrings a, b and c are interpreted as ordinary integers. My answer so far: Assume L is context-free. Then the pumping lemma for…
Catrina
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Is bin(n)bin(2^(k+1) * n + 1)^R context free?

bin is shortest number in binary Is bin(n)bin(2^(k+1) * n + 1)^R context free? k,n belongs to natural numbers. I know bin(n)bin(n + 1)^R is context free but I don't have idea how to solve bin(n)bin(2^(k+1) * n + 1)^R . If is context-free can…
PoliteMan
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How to prove a Language is NOT Context Free

I've been watching a lot of videos about how to prove this and I am getting mixed information about how to do so. In the case of contradiction, I am getting two different approaches and I want to know which is correct. Example: L = {a^n b^n+1…
msc
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Design a language L such that neither L nor its complement has an infinite regular subset?

I'm having a class on automata theory, and right now we are learning the pumping lemma. There is an exercise question asking us to "Design a language L such that neither L nor its complement has an infinite regular subset?" But I don't understand…
Eagle
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Relation of pumping lengths between related regular languages

How does the pumping length of a regular language relate to the pumping length of a related language. For example, if A :< B :< C are all regular languages and k is the pumping length of B, do we know anything about the pumping lengths of A and…
Jim Newton
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Regular languages and pumping lemma

I'm struggling to solve the following problems. I'm supposed to use the pumping lemma or regular language closures, but I just can't come up with a solution for these 2 problems. Any insight would be highly appreciate it. Thanks. For each language…
topstarterrhp
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Pumping lemma to prove a language is not regular

Hi I am trying to do practice questions for pumping lemma. I need to prove that the language L = {w E alphabet a,b,c | there are twice as many as as bs and twice as many bs than cs in w} Now i created a word w = a^4n * b^2n * c^n which belongs to L.…
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A detail on the Pumping Lemma for regular languages

I have one small question about the pumping lemma for regular languages - is it good enough to show that if a specific string belonging to a language L can't be pumped, then the language is irregular? For example - if I choose language L1 being of…
sparkFinder
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Pumping Lemma in context-free languages

A = {0^a 1^b 2^c | a < b < c} I need to show that A is not context-free. I'm guessing I have to use the Pumping Lemma for this, but how?
Clint
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Proof a language is not regular using Pumping Lemma

I am trying to prove that the following language is not regular using the pumping lemma. L = {ak b3l al | k ≥ 1 , l ≥ 0} I have decided to choose w = a b3p ap, then |w| = 4p+1 ≥ p Any tips? Thank you!
Aln
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Quick/Simple Regex/Regular Language Clarification

I feel like a moron posting such simple questions on here, but the knowledge base of this site is just amazing. Thanks for your understanding. Concerning a question about finding the minimum pumping length (concerning the pumping lemma for regular…
prelic
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How to determine whether given language is regular or not(by just looking at the language)?

Is there any trick to guess if a language is regular by just looking at the language? In order to choose proof methods, I have to have some hypothesis at first. Do you know any hints/patterns required to reduce time consumption in solving long…
Shubham Pandey
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Is the language L generated by 'Fibonacci Strings' (as given in the desciption) regular? If not, disprove by Pumping Lemma

The Fibonacci strings are defined as follows: S1=a, S2=b and Sk=S k-1S k-2 for k>2 . For example S3=ba , S4=bab etc . Let L be the language generated by the Fibonacci strings. Is the language‘ L ’ Regular? If not, disprove by Pumping Lemma.
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