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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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Proving if a language is context free with pumping lemma

I got a question on how to prove whether a language is context free using pumping lemma. Let's say language L. It contains a finite sequence of positive integers, it rises then falls (informally). Formally, we require that there exists k ∈ {1, 2, .…
Chaot1c
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How to prove that L = {a^j b^k c^k d^k: j, k ≥ 1} ∪ {b^j c^k d^l : j, k, l ≥ 0} satisfies the pumping lemma for CFL’s?

I have to prove that L satisfies the pumping lemma for CFL’s. The language L is not context-free but satisfies the pumping lemma for context-free languages. Let L be : L = {a^j b^k c^k d^k: j, k ≥ 1} ∪ {b^j c^k d^l : j, k, l ≥ 0} I have previously…
Jon Silver
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Show is not regular with pumping lemma

I need help on this pumping lemma case: L_1 :={a^n b^m c^k | n = m or k = 0} Can someone explain how to handle k=0? I started with abc^n, but I don't know how to split this in uvw.
Saddam abi
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Why do we use pumping lemma to prove the non-regularity of languages? WHY?

I am currently working on the usage of pumping lemma and I need to know why do we use pumping lemma? the main question asked is why? I know we can prove the non-regularity and I know the formula/proof as well, I'd just like to ask why?
Abdul Ahad Akram
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Is the language L ={a^n b^k c^m | k>=0, n>m} regular?

I have to explain using the pummping-lemma that the language: L ={a^n b^k c^m | k>=0, n>m} is not regular. Can someone please explain how it is done on this particular language?
Ervin Cosic
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Using the pumping lemma to prove irregularity in a regular language - where is the error

I have a vital misunderstanding of the pumping lemma. In the following example I show an example of using it on a regular language to come to incorrect conclusions. What am I doing wrong? L={a*b*}, assume the language is regular so by the pumping…
Karl
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Is the pumping lemma proof wrong from book ?

The proof for 'pumping lemma' from book : Pumping lemma: If A is a regular language, then there is a number p (the pumping length) where if s is any string in A of length at least p, then s may be divided…
Anonemous
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Is this proof with the pumping lemma (no regular language) ok?

I need to proof that a given language is not regular, could this work? The language is M={a^m a^l c b^(m+l)|m,l in N} with the alphabet = {a,b,c}. Proof: Be n in N arbitrary but firm. We choose the word w=a^(2n)cb^(2n) with w in M and |w|>=n. Be…
Lisa.Neust
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L = { a^n b^n c^m d^m : n >= 1, m >= 1 } U { a^n b^m c^m d^n : n >= 1, m >= 1 } isRegular?

there is a lot of examples for pumpinglemma proof, but I did not figure out this, can anyone help ? L= { a^n b^n c^m d^m : n >= 1, m >= 1 } U { a^n b^m c^m d^n : n >= 1, m >= 1 }
John Nick
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Finding errors in pumping lemma conditions

In my exam, i was supposed to write all pumping lemma conditions. that exactly what i did : a friend told me that there is some errors but i can't find them... Can some one help please ? what are the errors & why ?
Mooh
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Pumping Lemma for Regular Languages for a language that includes a constant

If I have a language like this: L1 = {a^128 b^n a^n | n >= 0} and I have to prove it is not regular, is it enough to prove b^n a^n is not regular, thus the whole expression is not regular, since a^128 is finite?
krystal
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CFL Pumping Lemma L = {a^n b^m c^k d^k | n>m}

I have some troubles solving this exercise with context free pumping lemma. Can someone help?
Kwr93
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Prove that the following language is not a context-free

L = {a^i b^j c^k; i≠j and i≠k and j≠k}. First approach: I tried two different string to prove it by pumping lemma but non of them is correct. first w = a^m b^m+1 c^m+2 and m is pumping length. for example one case in w = uvxyz is that vxy in is a…
Pedram
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Context free language (Pumping lemma a^n b^m c^min(n,m))

I'm struggling to solve the following problem. I'm supposed to use the pumping lemma. To prove {a^n b^m c^min(n,m) | m,n >= 0 } is not Context Free.
user8891173
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Which part of the pumping lemma theorem for reg languages indicate whether I'm pumping in or out and how many times I pumped in/out?

Exam coming up and prof wants these info included. I understand how the lemma works but I can't conceptualize how the "pumping" happens in terms of in or out and how many times.
negative.25
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