Questions tagged [kleene-star]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
15
votes
2answers
3k views

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 ...
2
votes
3answers
91 views

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}$^*$. ...
2
votes
1answer
546 views

Is the Kleene star of an intersection contained in the intersection of Kleene stars?

I need to find if given two formal languages $L_1$ and $L_2$ $$(L_1 \cap L_2)^*\subseteq (L_1^* \cap L_2^*) $$ I think that it's true since this can be rewritten as $$ \bigcup^\infty_{i=0}(L_1 \cap ...
-3
votes
1answer
244 views

Is the set of all strings over a finite alphabet finite? [closed]

Suppose $Σ=\{0,1\}$; then $Σ^*$ is the set of all strings over $Σ$. Is $Σ^*$ over $Σ$ finte?