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I am writing a paper which use two different operations on sets of works $X$, both of which I want to denote by a star, $X^{\ast}$. One of these operations is the Kleene star, and for whatever reason I would like to keep the other operation as a star and change my notation for the Kleene star operation. Therefore, I was wondering if there is another, (relatively-commonly-used) notation for the Kleene star?

(This is not my area. I have read about a bit but not found any other notation. Also, I do realise that changing the notation of something with "star" in its name is...odd...)

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    $\begingroup$ Nobody uses any other notation for Kleene star. $\endgroup$
    – Benjamin Steinberg
    Commented Jun 20, 2017 at 11:36
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    $\begingroup$ $X^\ast$ = Kleene star, ${}^\ast\! X$ = user111368 star. $\endgroup$
    – Carlo Beenakker
    Commented Jun 20, 2017 at 11:51
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    $\begingroup$ Let me add that in any context in which you are using $X^+$ notation or other regular expression notation (en.wikipedia.org/wiki/Regular_expression), then it would be confusing to use $X^*$ to mean anything other than the Kleene star. $\endgroup$
    – Joel David Hamkins
    Commented Jun 20, 2017 at 13:28
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    $\begingroup$ You will definitely confuse language theorist with any other use of * in the paper. I got in trouble once because I accidentally used Kleene star and the notation $\mathbb Q^*=\mathbb Q-\{0\}$ in the same paper. $\endgroup$
    – Benjamin Steinberg
    Commented Jun 20, 2017 at 13:51
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    $\begingroup$ I'd advise against using $X^*$ with a strange meaning and $X^+$ as Joel says. $\endgroup$
    – Benjamin Steinberg
    Commented Jun 20, 2017 at 13:52

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$X^*$ simply is the submonoid generated by $X$ of the free monoid of words over some alphabet, hence you could use the notation $\langle X\rangle$.

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    $\begingroup$ Care to explain the downvotes? $\endgroup$
    – Michaël
    Commented Jul 2, 2017 at 12:28

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