On polynomial recursive sequences [article]

Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk, Géraud Sénizergues
2020 arXiv   pre-print
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.
arXiv:2002.08630v1 fatcat:mle5zy7lgbhotmcrnl63ywteyu