I can't find anywhere the meaning of $L^*$, given that $L$ is a language. I know $^* $ means repetition, for example $0^*$ = $\{ \epsilon, 0, 00, 000, \dots \}$. Or if $A$ is an alphabet $A^*$ are all the possible words.

Does $L^*$ mean the language whose words are the concatenation of the words of $L$?

For example if $L=\{ 01^n \mid n>0 \}$

then is $L^* = \{ 01^{n_1}01^{n_2} \dots \mid n_1>0, n_2>0, ... \} $?

  • $\begingroup$ $L^\ast = \bigcup_{i=0}^\infty L^i$, where $L^i = \{ w_1 \cdots w_i \mid w_1, \ldots, w_i \in L \}$. See also here. $\endgroup$ – dkaeae Jul 3 '19 at 13:05
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    $\begingroup$ @dkaeae Please don't answer in comments. $\endgroup$ – David Richerby Jul 3 '19 at 14:02

Given a language $L$, let $L_0 = \{\epsilon\}$ and, for $i\geq 1$, let $L_i = \{w_1\circ \dots\circ w_i \mid w_j\in L \text{ for each } j\}$, where $\circ$ denotes concatenation. Then the Kleene closure of $L$ is the language $L^* = \bigcup_{i\geq 0} L_i$.

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