149 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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### Why is this not recognized by a DFA?

I am still confused over my professor's explanation on why this problem is not a DFA. The Problem: Explain why $L = \{p^kq^k \mid k>0\}$ cannot be recognized by a DFA My professor explained it as ...
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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 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 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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### 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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### 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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### 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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### 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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### Language of strings of lengths that are prime is regular? Is C^* regular? [duplicate]

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?...
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### Using Nerode theorem to prove that the following languages are non-regular

I've been trying to understand the idea behind proving a language is not regular by using Nerode's theorem, but I just couldn't apply the idea on what I've been asked. The problem is to prove the ...
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### Pumping lemma for non regular languages [duplicate]

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 ...

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