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- W1999497788 abstract "A set $Xsubseteqmathbb N$ is S-recognizable for an abstract numeration system S if the set $rep_S(X)$ of its representations is accepted by a finite automaton. We show that the growth function of an S-recognizable set is always either $Theta((log(n))^{c-df}n^f)$ where $c,dinmathbb N$ and $fge 1$, or $Theta(n^r theta^{Theta(n^q)})$, where $r,qinmathbb Q$ with $qle 1$. If the number of words of length n in the numeration language is bounded by a polynomial, then the growth function of an S-recognizable set is $Theta(n^r)$, where $rin mathbb Q$ with $rge 1$. Furthermore, for every $rin mathbb Q$ with $rge 1$, we can provide an abstract numeration system S built on a polynomial language and an S-recognizable set such that the growth function of X is $Theta(n^r)$. For all positive integers k and l, we can also provide an abstract numeration system S built on a exponential language and an S-recognizable set such that the growth function of X is $Theta((log(n))^k n^l)$." @default.
- W1999497788 created "2016-06-24" @default.
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- W1999497788 date "2010-12-30" @default.
- W1999497788 modified "2023-09-27" @default.
- W1999497788 title "The growth function of S-recognizable sets" @default.
- W1999497788 hasPublicationYear "2010" @default.
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