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Journal Articles Theory of Computing Systems Year : 2021

On Polynomial Recursive Sequences

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.

Dates and versions

hal-03467171 , version 1 (06-12-2021)

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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⟩
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