163 questions linked to/from How to prove that a language is not regular?
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### Show that {xy : x,y ∈ {a,b}*, |x| = |y|, x ≠ y} is a not a regular language

Actually, I know that there are many examples showing how this is a contex-free language, but I can't find any that show it isn't regular. I would appreciate if I could have a solution step by step ...
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### Show that $\{xy : x \in \{a\}^*, y \in \{b\}^*, |x| = |y|\}$ is a not a regular language

I have been asked as an exercise how to prove that this is not a regular language. first I tried to use the pumping lemma, but I got stucked. Th erxercise hust said to prove thata this isn't a regular ...
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### How to check $L$ is regular or not [duplicate]

If $L=\{w \in \Sigma^*\mid w=uv,\text{ number of occurnce a's in$u$equal to number of occurrence b's in$v$}\}.$ I think $L=\Sigma^*$ because for any string in $\Sigma^*$, we can split it to $uv$ ...
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### Prove a language is not regular without pumping lemma [duplicate]

How can you prove that $L=\{a^n b^{2n} \}$ is not regular without the use of pumping lemma?
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### Is $\{a^mb^nc^n \mid m,n \geq 0\} \cup \{b,c\}^*$ regular or not?

Show if $L = \{a^mb^nc^n \mid m,n \geq 0\} \cup \{b,c\}^*$ is regular or not. My attempt: I think the Pumping lemma won't work in that constellation, so I'm working with "The intersection of ...
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### How to prove a language isn't necessarily regular? [duplicate]

Assuming we have a regular language $L$, how can we prove that $L'= \{ xz \mid \exists y : xyz \in L \text{ and } |x|=|y|=|z|\}$ isn't necessarily regular. So far I can't come up with much for how to ...
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### Is that a regular express? Proof using closure properties or pumping theorem [duplicate]

I am studying regular express. I understand how to proof a xa ya. However, I don't know how to proof the below problem. Please help me. L = { xa yb | a ≠ b }
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### Proving of regular language [duplicate]

Is this regular or not L = {w1w^R | w ∈ {0,1}* (where for any word w ∈ {0,1})*, w^R denotes the reverse of w)
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### Is this language L regular?

Let's say we have the language L = {w $\in$ {a,b}$^*$ : ($\exists n \in \mathbb{N}$)[$w|_b = 5^n$]}. I want to know if this is a regular language or not. How do I go about doing this? I'm familiar ...
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### Prove its not a regular language [duplicate]

I have a question. Assume $L = \{ a^m b^m \mid m ≥ 1 \}$ is not a regular language. Prove that $I = \{ a^{5n} b^{3m} c^n d^m \mid m,n ≥ 0 \}$ is not a regular language. I can prove it with pumping ...
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### Prove that the following language is not regular: $\{0^i1^j : i \neq j\}$ [duplicate]

I was trying to approach this proof, after multiple reads and attempts I am getting nowhere. If someone could help me out that would be great. Should I use the pumping lemma, if so how show I start, ...
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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 [duplicate]

This is a question I've been asked to do and I honestly have no idea how to approach this. Help please?:)
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### Proving a language is Not Regular without using Pumping Lemma? [duplicate]

I was wondering how one would go about proving a language is Not Regular without using the traditional pumping lemma contradiction. $$L = \{ 1^k 0^n 1^n 0^k \mid k \geq 0, n \geq 0\}$$ I've seen a ...