152 questions linked to/from How to prove that a language is not regular?
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### Proving that language, with $|\Sigma|=1$, is irregular by Myhill–Nerode theorem

We have $\Sigma =\{0\}$ and $$L=\{0^{2^n} \mid n\ge 0\}$$ How to prove that $L$ is irregular by using Myhill–Nerode theorem? At other languages with $\Sigma >1$ we can usually separate the word or ...
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### Is this the correct way to use the pumping lemma?

I've been watching lectures from Coderisland on YouTube about finite state machines, DFAs and NFAs, and in one discussion he talks about how to use the pumping lemma to show how a language is not ...
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### Proving that $L = \{ a^{n!} \ | \ n \geq 0 \}$ is not regular

Let $L$ a language over $X = \{a\}$ defined as follow : $$L = \{ a^{n!} \ | \ n \geq 0 \}$$ I want to prove that $L$ isn't regular, I have searched in the forum for an equivalent question, but I ...
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### Is the language of all DFAs that accept the empty language regular?

Is $E_{DFA}$ in the class of regular languages? $\qquad E_{DFA} = \{ \langle D \rangle \mid D \text{ is a DFA }, L(D) = \emptyset\}$ My argument is that it is because all of the DFAs in $E_{DFA}$ ...
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### Proving $L = \{a^iba^j|i\ge2j\ge0\}$ isn't regular

I need to prove the following language is not regular, I think I need to use the pumping lemma. The trouble I am having is that there is multiple variables and I am not used to that. Could someone ...
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### Proving that $a^{2^kp}$ isn't context-free (where $p$ goes over all primes)

I have this language and have to prove that its not context free: $$L = \{a^{2^kp } \mid k \in \mathbb{N}, p \text{ is prime number}\}.$$ Because it's unary, a context free language is also regular, ...
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### How to choose a word to apply the Pumping Lemma?

I have some questions about the PUMPING LEMMA. First of all, I do not study computer science, I still go to school, but I'm very interested, so I could make mistakes. And sorry about my English :) ...
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### How to show that the language made up of strings with nlogn 0s is not regular with the pumping lemma?

How to show that the following language is not regular with the pumping lemma? $$L=\left\{0^{n\lceil\log_2 n\rceil} \,\middle|\, n\in \mathbb{N}-\{0\}\right\}.$$
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### DFA for $L = \{y \in (a+b)^* \mid ||y|_a - |y|_b| \leq 10 \}$

$L = \{y \in (a+b)^* \mid ||y|_a - |y|_b| \leq 10 \}$ Any idea? I have problem with this kind of task.
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### Use the pumping lemma to show that the language is not regular [closed]

I am working on this problem : Use the pumping lemma to show that the language $\{0^n 1^{n} \mid n ≥ 1\}$ is not regular. May someone give me some suggestion about how to solve this problem?
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### How to prove that the language of words ucv with as many a's in u as b's in v is irregular?

I'm trying to prove that: $L=\{w\in\{a,b,c\}^*\Big|\#_a(u)=\#_b(v),\ \ w=ucv,\ \ \ u,v\in\{a,b\}^*\}$ is irregular, so I'm trying to use the Pumping Lemma. This is what I tried so far: $w=a^ncb^n$...
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### proving L = {$a^{100}yy^r : \forall y \in$ {a,b}*} is not regular

I need to prove that L = {$a^{100}yy^r : \forall y \in$ {a,b}*} is not regular. i have tried using pumping lemma but couldn't get far with it. Any help in where i should go with it?
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### The alphabet is {a, b}. Show that the set of words with the same number of occurrences of a and b is not regular

This is a question I've been asked to do and I honestly have no idea how to approach this. Help please?:)
With $\Sigma = \{a\}$ I want to see if a language $C = \{a^p \ | \ p \ \text{is prime}\}$ is regular and whether or not $C^*$ is regular. How would I go about showing whether $C$ or $C^*$ are regular?...