Necessary properties of formal langagues in certain classes that rely on closure against repetition of certain subwords. Make sure your question isn't covered by applying the techniques in https://cs.stackexchange.com/q/1031/755.
Questions tagged [pumping-lemma]
549 questions
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Factorial usage within proof using the pumping lemma
We are going over the pumping lemma in class and we recently went over the following example:
Let
$$ L = \{ w \mid w \text{ has a different number of 0s and 1s} \} $$
Consider
$$
s = 0^P1^\left(P+P!\right)
$$
$ s $ can be divided into $ s = xyz…
Bryan Roth
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Pumping Lemma for $L = \left \{ a^{c}\mid \text{c is a composite number} \right \}$
$L = \left \{ a^{c}\mid \text{c is a composite number} \right \}$
I feel that this is not a context-free language as checking this constraint requires divisibility checking, but I am facing a hard time in proving that $L$ is not a Context Free…
Romy
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1 answer
Is the language $L = \{a^nb^m : n = 2^m\}$ context-free?
Is the language $L = \{a^nb^m : n = 2^m\}$ context-free?
Assume L is a context-free language. Then $\ \exists p\in \mathbb{Z}^{+}:\forall s\in L\left | s \right |\geq p. s = uvxyz,\left | vy \right |\geq 1,\left | vxy \right |\leq p. s_i =…
nestharus
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Pumping Lemma Question
I have been trying to solve this question and am kinda stuck. Wondering on how to proceed and finish this proof. Prove that the language $ L = \{a^{2^n} | n >= 0\} $ is not regular. I have been trying to use the pumping lemma but am stuck…
Cuthnard
- 11
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vote
2 answers
Why does Michael Sipser state that $0^p0^p$ is a bad choice for proving $L=\{ww|w \in \{0,1\}^*\}$ is non-regular a bad choice?
I feel that choice should work great for proving non - regularity of the mentioned language.
If $L=\{ww|w \in \{0,1\}^*\}$ and we choose $s=0^p0^p$, meaning s is atleast as long as 'p'. Then we can decompose s as follows $x=empty \ string,\ y =…
Pratik Hadawale
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How does Sipser's proof that $0^n1^n$ is not regular work?
In Sipser's Introduction to the Theory of Computation this is how $0^n1^n$ is proved to be not regular
Example 1.73:
Let $B$ be the language $\{0^n1^n|n \ge 0\}$
We use the pumping lemma to prove that $B$ is not regular. The proof is by…
Fackelmann
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vote
2 answers
What is wrong with this proof that proves that 0*1* is not a regular language?
I know why cases 1 and 2 are wrong because our language can have different numbers of 0's and 1's. But I'm not sure how case 3 can be proved wrong for our language.
Exercise 1.30:
Describe the error in the following “proof” that $0^{∗}1^{∗}$ is not…
Ellie
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vote
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Is there a human-friendly version of the Pumping-Lemma?
I found this on Wikipedia and I'm confused by the parenthesis in the notation not that it doesn't make sense to me but is there a more natural human version? And im generally confused about all the different notations surrounding logic and…
phiStackOverFlow
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When does $p$ break the pumping lemma
I want to prove that $\{A^iB^jC^k \mid i=j \text{ or } j=k\}$ is a not a regular language using the pumping lemma.
I've found that the only way to obtain a contradiction is when $x \in A^*$, $y \in B^*$, $z \in C^*$,
as $y$ is unable to be pumped…
Tengu
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vote
1 answer
How can I prove the minimum pumping length of finite language?
Let L be the set of all strings over {0, 1} whose lengths are at most three. Since L is regular, the pumping lemma holds for L, and thus there is a pumping length p associated with L. What is the smallest possible pumping length associated with…
AABBCC
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Pumping lemma for non regular languages
I read that pumping lemma is sufficient condition to prove non regularity of languages but not necessary condition.
I know the first part that it is sufficient is true but not able to understand why is it not necessary. Can someone please help me…
Sagar P
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Pumping lemma of regular language
I was wondering in how to solve this question, I feel a bit confused: for $\Sigma = \{1,\#\}$, consider
$$D=\{w \mid w=x_1 \# x_2 \# \cdots \# x_k \text{ for } k \geq 0, \text{ each } x_i \in 1^*, \text{ and } x_i \neq x_j \text{ for } i \neq…
bb12
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Pumping lemma not regular
How would about proving this is not regular with the pumping lemma. Please include all steps and explain all steps. I am really new with this.
$1^{2x}0^y$ and $y>= x$
Does it matter which side you pump? How do you pick which side to pump?
This is…
cokedude
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pumping lemma misunderstanding
given this information of a language I need to determine if the language is regular or not:
I thought to Assume by way of contradiction that L6 satisfies the conditions of the pumping lemma. Let p be the pumping constant. Consider the word w =…
user1701057
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Proving $L=\{wvw|v\in \{0,1\}^*, w\in \{0,1\}^+\}$ is not regular using the myhill-nerode and pumping lemma
Firstly, I've tried assuming $L$ is regular and find a contradiction with help of the pumping lemma's 3 conditions, I was not able to get to a contradiction.
I've tried thinking of a word $z\in \{0,1\}^*$ to attach to $wv^i$ and $wv^j$ for some…
Aishgadol
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