Questions tagged [kleene-star]
55 questions
17
votes
2 answers
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 able to intuitively grasp this concept because the…
Sagnik
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12
votes
3 answers
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 operations (concatenation, union, and star) for that…
user3295674
- 383
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7
votes
3 answers
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?
user6268553
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5
votes
0 answers
Regular languages for which star height is not increased by complementation
The set of (non-generalized) regular expressions over an alphabet $\Sigma$ is the set of expressions generated by the following grammar, where $a\in \Sigma$ ranges over symbols in the alphabet:
$$
\pi ::= \epsilon \mid \emptyset \mid a \mid…
Tom
- 51
- 2
5
votes
2 answers
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 since we can take some non-context free language…
AlexPatterson
- 53
- 4
3
votes
1 answer
Finding $L^*$ when $L=\{a^nb^n | n \geq 1\}$
Let $L=\{a^nb^n | n \ge 1\}$, then $L^\star=L^0 \cup L^1 \cup L^2 \cup L^3 \cup \dots = \{\epsilon\} \cup \{a^nb^n\} \cup L^2 \cup L^3 \cup \cdots$ .
How to find $L^2$ and $L^3$, and is $L^2=\{a^nb^na^nb^n\}$? In this video…
Basem Majed
- 33
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3
votes
4 answers
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 there can be no string in the language that…
Chris F.
- 61
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3
votes
2 answers
How to show closure of regular languages without DFA,NFA,reg expressions
Given a $\Sigma$ I define a regular language as one of the folllows:
$\emptyset$
$\left\{ \sigma \right\}$ for any $\sigma \in \Sigma$
$L_1 \cup L_2$ for regular $L_1, L_2$
$L_1 \cdot L_2 $ for regular $L_1,L_2$
$L^*$ for regular $L$
Now, I would…
Eric_
- 535
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3
votes
1 answer
Why do we need two variables for implementing kleene star operation on a language using context free grammars?
I have a Context-Free Grammar (CFG) G which has a S for generating a language L. Now to produce a grammar for L*, another variable T (which is not present in the variable set of G) is taken and the grammar is produced in the following way:
…
killua
- 33
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3
votes
1 answer
How is $L^* - \{\epsilon \} \neq L^+$?
I was asked which among the following is true:
$\Sigma^*-\{\epsilon\} = \Sigma^+$
$L^* - \{\epsilon \} = L^+$
As I can see, both $\Sigma^*$ & $L^*$ are sets. I thought both were true because of set difference, but the answer lists only the…
Mr. Sigma.
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2
votes
2 answers
How to Apply Elementary Axioms from Kleene Star to an Inequality
Axioms For *
\begin{align}
1 + aa^* &\leq a^* \\
1 + a^*a &\leq a^* \\
b + ax &\leq x \to a^*b \leq x \\
b + xa &\leq x \to ba^* \leq x \\
\end{align}
Elementary Results
\begin{align}
a \leq b &\to a + c \leq b + c \\
a \leq b &\to ac \leq bc\,…
grant2088
- 37
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2
votes
1 answer
Does the set $\{10^n \mid n\geq1\}^*$ include $10100$?
Consider the following set constructed with a regular Kleene-star operation:
$$
\{10^n \mid n\geq1\}^*
$$
Would something like $10100$ be in this set? I know $1010,100100100,1000,$ etc would be, but I'm not sure if you can change $n$ per repetition…
Leorio Paradinight
- 59
- 1
2
votes
3 answers
When is the empty word part of $A^+$?
My professor mentioned the below statement in class but without a proof. I am trying to prove it for myself as I don't understand 100% why this is always the case.
Given is A, a subset of {0,1}$^*$.
ε $\in\ A^+$ <-> ε $\in\ A$, where ε is the empty…
cndolo
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2
votes
1 answer
Prove that $L$ is closed under Kleene star iff $L=NL$
Prove that $L$ is closed under Kleene star iff $L=NL$
Hi,
I am trying to solve this exercise, but it is quiet difficult.
Of course first part is very easy:
Let assume that $L=NL$. Lets consider language $A\in L$. We show that also $A^*\in L$. It…
Haskell Fun
- 379
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2
votes
1 answer
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.
I answered that only 2 implies 1 but the answer is…
user779444
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