On polynomial recursive sequences
Formal Languages and Automata Theory
2020-02-21 v1
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.
Cite
@article{arxiv.2002.08630,
title = {On polynomial recursive sequences},
author = {Michaël Cadilhac and Filip Mazowiecki and Charles Paperman and Michał Pilipczuk and Géraud Sénizergues},
journal= {arXiv preprint arXiv:2002.08630},
year = {2020}
}