Questions tagged [pumping-lemma]
224 questions
12
votes
1 answer
The “Pumping Lemma” For Finite Monoids
Let $M$ be a finite monoid. I’m trying to prove the following: there is a constant $N$ such that if $n \geq N$ and $m_1, \ldots, m_n \in M$, then some subword of $m_1 \cdots m_n$ is an idempotent. (This is analogous to the classic pumping lemma for…
neddo
- 215
6
votes
2 answers
Pumping Lemma for $L= \{a^{m}b^{n}| m,n > 0 , \gcd(m,n) > 1 \}$
Let language $L= \{a^mb^n \mid m,n > 0 , \gcd(m,n) > 1\} $ above the alphabet $\Sigma = \{a,b\} $ .
I need to prove by the pumping lemma that $L$ is not a regular language but I am having trouble finding a string I can pump resulting in the string…
A-H
- 149
5
votes
2 answers
What is wrong with my pumping lemma proof?
Here I am going to give a proof that L = {w | w is an element of {0,1}* and w has an even number of 1's} is not regular (even though it is regular) and I would like someone to point out what is wrong with my proof.
This is a regular language…
James S
- 63
5
votes
1 answer
How can I prove that this language is not context free?
The language is $A = \{a^{n}b^{n}a^{m} : n \geq 0, m \geq 0, n \neq m\}$.
I tried to use the pumping lemma. I chose the string s = $a^p b^pa^{p + p!}$ that is split in $uvxyz$ and must respect
$|vy| > 0$
$|vxy| \leq p$
$uv^ixy^iz \in A, i \in…
FY Gamer
- 303
4
votes
1 answer
Searching for a proof for a variant of the pumping lemma for context free languages
So I'm trying to understand the pumping lemma for CFL ( context free languages ).I've already used it to show that a language is not contextfree and I have considered the proof of this lemma (see the PDF below ) Now I've read that there is a variant…
Mugumble
- 1,184
3
votes
1 answer
Pumping Lemma for regular languages proof template
http://www.cs.uiuc.edu/class/fa06/cs273/Lectures/pumping-lemma/pumping-lemma.html
So, I went to that site and it says:
$w = xyz$
$|xy| \leq p$
$|y| \geq 1$
for all $i$, $xy^iz$ is in $L$.
There exists a string $w^p$ in $L$ of length at least $p$…
user539484
- 245
3
votes
1 answer
Check if the Language is context-free using the Pumping Lemma
$$
L=\{a^ib^jc^k \mid i, j, k \in N \text{ and } i
kklaw
- 311
3
votes
1 answer
Using Pumping Lemma for Context Free Languages
Pumming Lemma Question -Not Context Free
I understand the general concept of pumping lemma but I don't quite understand how to write proofs formally. In this particular case (see image attached),I understand that:
if we divide it into $uvxyz$ and…
x89
- 189
3
votes
1 answer
Pumping lemma for regular language
On an exam we got this question:
Let $B = \{w \in \{a,b\}^* : w \neq w^{rev}\}$
Prove $B$ is not regular.
I only got 1 of 4 pts on this question and the teachers comments are below.
My solution:
Assume $B$ is regular then $B$ has a pumping length…
automatatheoriesq
- 41
- 3
3
votes
1 answer
proving {$a^ib^jc^k |\;j=i\;or\;j=k$} is not regular
{$a^ib^jc^k |\;j=i\;or\;j=k$} what i tried so far was first splitting it into {$a^ib^jc^k |\;j=i$} or {$a^ib^jc^k |\;j=k$} then tried to use the pumping lemma to prove it. However i couldnt get very far with it. Any help is appreciated, thanks
Jenny
- 31
- 1
3
votes
2 answers
Prove that the language is not regular using pumping lemma
Could anyone explain me how to prove that this language is not regular using pumping lemma? I can prove easier examples but with this one I do not even know with which word i should start proving it.
$$
L = \left\{ aavau \mid u,v \in \{b,c\}^*…
kvway
- 195
3
votes
2 answers
Prove that $\{w \mid \text{ w has even length and the first half of w has more 0s than the second half of w} \}$ is not regular?
I have had some difficulties understanding proofs that a language is not regular using the Pumping Lemma, and now I need to prove that the following language
$$A = \{w \mid \text{ w has even length and the first half of w has more 0s than the…
user168764
2
votes
1 answer
disprove $L = \{ a^nb^n\mid n \geq 0 \}$ is not a context-free using Pumping Lemma for Context-Free Languages
I am writing something about Pumping Lemma. I know that the language $L = \{ a^nb^n\mid n \geq 0 \}$ is context-free. But I don't understand how this language satisfies the conditions of Pumping Lemma (for context-free languages)?
If $z=a^mb^m$…
Harish
- 149
2
votes
1 answer
It is a correct proof? Pumping lemma
Let :
$
L = \{ w = \{0,1\}^* | w = 1^k \textrm{ or } w = 0^j {1^k}^2, j >= 1, k>=0 \}
$
So i split that language into L1 and L2 languages and treated them separately.The first one $(1^k)$ is for sure regular.
Second language is a bit of a problem…
Eri
- 23
2
votes
0 answers
Identifying whether certain palindromic languages are non-regular
In a nationwide entrance exam conducted in India, the following problem was asked in the year 2007:
Which of the following languages are regular?
(A) $L_1 = \left\{ ww^R \mid w \in \{0, 1\}^+ \right\}$
(B) $L_2 = \left\{ ww^Rx \mid x,w \in \{0,…
Harsh Pathak
- 21