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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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Contextfree language or not? I can write a grammar but not use pumping lemma

I have the language: L = {0^i 1^i | i >= 0} The grammar that describes it proves it is a context free language: S -> 0S1 | e If a language is context free, Pumping Lemma should hold. I can however not get it to work, no matter what i…
Kent Munthe Caspersen
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Pumping Lemma, Condition 1

Let B be the language {0n1n | n >= 0} i.e. 0 and 1 has to have the same length Let s in B be the string 0p1p Assume B is regular so s must be divisible to s = xyz where xyiz i>=0 is still in B (Condition 1 of three conditions of pumping…
antz
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Proving that the language is regular or not

We use pumping lemma for regular languages to find a language is regular or not. There is a question in the homework that I don't know how to apply pumping lemma onto the language. L = {a$b: a,b ∈ {0,1}*, number of zeroes in a equals to the number…
gzg
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Pumping Lemma and Hierachy

I have a question involving the Pumping Lemma for Regular Languages and Pumping Lemma for Context-free Languages: Is it possible that there's a language which doesn't meet the criteria for the pumping-lemma for context-free languages but does meet…
SmallBrainStudent
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Using string of set length with pumping lemma to prove irregularity

There is this proof that I thought of that I am not quite sure if it's valid or not. Suppose you had to prove the nonregularity of the following language: A = { 0^n 1^n 2^n | n>= 0 } The proof I devised picks a string that belongs in the language,…
Mr Bones
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Is it possible to prove that L is a regular language?

Let L = {a^f(m) | m >= 1 } where f: Z^+ -> Z^+ is monotone increasing and complies that for all element n in Z^+ there is an m belonging to Z^+ such that f(m+1) - f(m) >= n. Is it possible to prove that L is a regular language?
Alejandro Barreiro
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Is L = {ww^Ru | w, u ∈ {0,1}+} regular language?

let L = {wwRu | w, u ∈ {0,1}+}. Is L regular language ? Note that w, u cannot be empty. I've tried to prove it is not regular language by the pumping lemma, but I failed when w = 0^p1^p, 01^p, (01)^p. Once I take y = 0^p or 1^p, xyyz will be…
Charles Zhang
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Regular language demonstration

Consider this function: Faro(x,z) that assume value: z if x = ε and a.faro(z,y) if x = ay So is a recursive function, and for instance we have as result of faro(00110, 0101) = 000110110 I have to demonstrate that if L and M are regular language on…
redsunflower
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How to prove a language with (ab)^n.. is not regular with pumping lemma?

I have been working to understand the pumpming lemma better but I am quite stuck at proving these 2 languages is not regular: L_1 = {(ab)^n c^m | n>=1, m>=2n } L_2 = {(ab)^n a^k (ba)^n | k<3} for the L_2 my approach was: Let's say there is a…
han chu
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How to read language definition syntax for regular/nonregular languages

I am trying to understand a simple concept about Language definition. Specifically when there are two strings in the language definition. such as: Language F = ww | w ∈ {0,1}* Can someone help me understand the syntax? It makes sense to me…
Kiefer_Michael
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Use the pumping lemma to show that the following languages are not regular languages L = {anbm | n = 2m}

Use the pumping lemma to show that the following languages are not regular languages L = {an bm | n = 2m}
alaa raed
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proof L = {a^n b^m | n>=m} is irregular language

I am stuck in finding S for pumping lemma. is there any idea to proof that L = {a^n b^m | n>=m} is an irregular language?
Mohammad Derakhshan
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How to Pumping lemma for Regular language

I have this problem that I need to prove that the language is not regular by using pumping lemma, but no matter how much I read how to do it, I still don't understand. Could someone please help how to solve this? Show that L = { a^n c b^m | n, m…
Saul
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Minimum pumping length of L= {0^i1^j | i >= j} to prove L is non regular

Both Mr. Mithlesh Upadhyay and You play a game: 1. Mr. Mithlesh Upadhyay gives you a constant n. 2. You choose a word w in the language of length at least n. 3. Mr. Mithlesh Upadhyay gives you x, y, and z with xyz = w, |xy|≤n, and y not empty. 4.…
Olivia Pearls
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how do we prove that this language is irregular using the pumping lemma?

while solving, I came across a tricky question that asked me to prove that a certain language is irregular using the pumping lemma. that question is as follows: prove that the language L is irregular using the pumping lemma, where L is a language…
Ahmed Mokhtar
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