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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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Basic Pumping Lemma proof doesn't make sense

Proving that a^n b^n, n >= 0, is non-regular. Using the string a^p b^p. Every example I've seen claims that y can either contain a's, b's, or both. But I don't see how y can contain anything other than a's, because if y contains any b's, then the…
Dave
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Pumping Lemma On Context Free Language

For the language {a^2^n | n >= 0} I understand that first some k is chosen, and then z = uvwxy such that vx != epsilon and #(vwx) <= k, but I can't think of any i which proves that this language is not context free.
VadislavBby
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Using third condition of Pumping Lemma to simplify proof

So I've got a homework question that asks to prove that A = {a^n b^n c^n | n >= 0} is non-regular using the pumping lemma. From my textbook: To use the pumping lemma to prove that a language B is not regular, first assume that B is >regular in…
BryanO
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Is this language regular? {0^n 1^m | m != n}, I don't understand the direct proof by pumping length

There is a direct way to prove it: If p is the pumping length and we take the string s = 0p1p+p!, then no matter what the decomposition s = xyz is the string xy1+p!/|y|z will equal 0p+p!1p+p! which is not in the language. I don't understand the…
Harshal Carpenter
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Understand the pumping lemma

I am relatively new to the pumping lemma, and I have a problem here that I think I answered correctly, can anyone tell me if this works and if not why not The problem: {www | w is {a,b}*} My approach: L = www u* (v^k) * w has to be a subset of L…
Guitardeon
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regular language pumping lemma for string with even 0's

find whether string with even number of zeros is a) context free b)regular a) using pumping lemma for CFL....it can be represented as e(0n)e(0n)e. so , it's a CFL. b) it can be represented as (00)* in regex. So, i think it's a regular language. But,…
claudius
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Pumping Lemma for languages with no order

I've been doing some problems from my textbook to practice for finals and I ran into one question I couldn't quite figure out. Basically it was for Let L = {w | w contains more 0's than 1's} And it says as a hint that the pumping lemma for regular…
user1777900
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Struggling to understand Myhill-Nerode

I think I know the pumping lemma and was told that Myhill-Nerode is a very elegant way to show that something is regular or not regular. But I am having a lot of trouble with it. Take this for example: = {0k, k = 2n, n >̲ 1} My language is the…
David Zorychta
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Is a^i^2 | i>=1 regular?

Though this expression, is accepted by deterministic finite automation, but if we applying pumping lemma on this expression, pumping lemma fails, also this expression have finite states but does not halt and run on continuously, the edges keep…
peeyush.cray
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Is it context-free language?

i have a problem with an exercise: L = {an bm cp | 1 <= n <= m <= p} Is it possible write a grammar for that exercise ? I do not understand how to solve it :( please help me
egos
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Tips to 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 = {ai bj | i = 2j for some j ≥ 0} I have decided to choose s = a2p bp, in this way |s| ≥ p and I can split it in three pieces xyz where for every i ≥ 0, xyiz…
colis
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Is this language regular? {a^i b^j| i=j mod 19}

I know that {a^i b^j | i = j } is not regular and I can prove with pumping lemma; similarly I can use pumping lemma to prove this one not regular too. But I think I see some similar problem that says such language is actually regular. And because…
Arch1tect
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Use pumping lemma to prove grammar is not context free?

I'm trying to prove that L={y#x|(y is a substring of x) ∧x,y∈{a,b}^* } is not context free using the pumping lemma, but I can't seem to do that. If |vy|≠ε ,|vxy|≤k , uv^n xy^n z∈L ,∀n≥0 Then either vxy has both a and b, or only b or only a. How…
JAN
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Context Free pumping lemma

Is the following language context free? L = {a^i b^k c^r d^s | i+s = k+r, i,k,r,s >= 0} I've tried to come up with a context free grammar to generate this but I can not, so I'm assuming its not context free. As for my proof through…
kbirk
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