# Questions tagged [kleene-star]

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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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### 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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### Will $L = \{a^* b^*\}$ be classified as a regular language?

Will $L = \{a^* b^*\}$ be classified as a regular language? I am confused because I know that $L = \{a^n b^n\}$ is not regular. What difference does the kleene star make?
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### Is a kind of reverse Kleene star of a context-free language context-free?

Recently I had a question on one of my assignments asking to prove or disprove the following: Let $L$ be a language. If $L^*$ is context-free then $L$ is context-free. Now obviously this is false ...
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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 Empty language

I had a test a couple of days ago and one of the question had 2 statements : $L^+ = L^\ast$ $L$ contains $\varepsilon$ I had to say does 1 imply 2, does 2 imply 1 or do they both imply each other. ...
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### Proving $(a+b)^* = b^*(ab^*)^*$ equationally

I am new to automata theory and have a problem in understanding equivalence of regular expressions, though I can go for the construction procedure of minimized DFAs to prove that both are equal. I ...
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### Lexicographic Order of Expression [Automata Theory]

what will be kleene star "expansion" of expression $a^*b^*$ in lexicographic order? I'm confused and I really want to clear my concepts so I can proceed further
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### Proving $A^\ast = A$ on a given set

I am working on some set theory and am trying to prove how a set can have the property $A^* = A$. For set $A=\{0^n1^n \mid n \ge0\}$, I still do not understand exactly what $A^*$ is. For example, I ...
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### Reflexive transitive closure = (zero or more) Kleene star?

In Alloy Tutorial they denote some reflexive transitive closure with Kleene star saying that they admit zero or more elements at that position. ...
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### Validity of some Kleene star statements [duplicate]

I'm taking an intro to computability course right now and I'm having some trouble with a couple examples that the professor doesn't seem too clear on. We're learning about languages and doing some ...
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### Why is DCFL not closed under kleene star? [duplicate]

I honestly haven't an idea how to proof that eventhough I can understand the background, could someone help me?
$L^*$ is the kleene star of L. say we have a def: $L^*$ = $L^0$ U $L^1$ U $L^2$ U ... U $L^K$ then prove that: $L^*$ = $L$ if and only if $L$ = $L$ o $L$ how do i prove this?
Suppose $Σ=\{0,1\}$; then $Σ^*$ is the set of all strings over $Σ$. Is $Σ^*$ over $Σ$ finte?