# Questions tagged [kleene-star]

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### Are regular expression a* and a.a* equal?

a* = {λ, a, aa, aaa, aaaa.....} a.a* = a.{λ, a, aa, aaa, aaaa.....} = {a, aa, aaa, aaaa, aaaaa....} Then these two regular expressions above should not be equivalent. Please correct me if i am wrong.
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### Regular languages that can't be expressed with only 2 regex operations

I thought all regular languages could be expressed with regular expressions (if a language is regular, it can be expressed with regex), but I have been told that you need all three of the regular ...
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### How to determine if a regular language L* exists

I'm trying to make sense of regular languages, operations on them, and Kleene operations. Let's say I define a language with the alphabet {x, y}. Let's further say that I place the restriction that ...
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### Kleene star differences

We have languages $A= \{a\}$ and $B = \{b\}$. If we consider $(A\cup B)^*$, where ${}^*$ means Kleene star, we have a set of words like $\{\lambda, a,b,aa,ab,aaa,\dots\}$, where $\lambda$ is the empty ...
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### Kleene star operation on the empty language

In my text book it is mentioned that: $\emptyset^*=\{\epsilon\}$ where $\emptyset$ is an empty language. However, we know that $L \cdot \emptyset = \emptyset$, where $L$ is any Language. I am not ...
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Suppose $Σ=\{0,1\}$; then $Σ^*$ is the set of all strings over $Σ$. Is $Σ^*$ over $Σ$ finte?
For a language $L\in\Sigma^*$ we define $$L^*=\{w\mid \exists k\in \mathbb{N}\cup\{0\}, ∃x_1,...,x_k\in L \ (w=x_1...x_k) \}$$ Let $L$ be a regular language over some alphabet $\Sigma$. Prove that \$...