On Polynomial Recursive Sequences

Michaël Cadilhac (1) , Filip Mazowiecki (2) , Charles Paperman (3, 4) , Michał Pilipczuk (5) , Géraud Sénizergues (6)

1 SOC - School of Computing [DePaul]
2 MPI - Max-Planck-Institut für Mathematik
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
4 LINKS - Linking Dynamic Data
5 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
6 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Domaines: Théorie et langage formel [cs.FL]

Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk, Géraud Sénizergues. On Polynomial Recursive Sequences. Theory of Computing Systems, 2021, ⟨10.1007/s00224-021-10046-9⟩. ⟨hal-03467171⟩