On polynomial recursive sequences
Abstract
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is $b_n=n!$. Our main result is that the sequence $u_n=n^n$ is not polynomial recursive.
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