On Polynomial Recursive Sequences

Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michal Pilipczuk, Géraud Sénizergues

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 = nⁿ is not polynomial recursive.