On Polynomial Recursive Sequences
Résumé
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.