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.
Feb 20, 2020
Feb 20, 2020 · We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences.
Write down for any a, p and all b = 1,2,3,...,l: P1(a) · Q1(a)1 + ... + Pl(a) · Ql(a)1 ≡ 0 mod p. P1(a) · Q1(a)2 + ... + Pl(a) · Ql(a)2 ≡ 0 mod p.
People also ask
What does recursive mean in polynomial?
What is an example of a recursive sequence?
What is the equation for recursive sequences?
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences.
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences ...
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences.
Oct 16, 2023 · We consider recursive sequences over the set of integers, where as rules of generation we take arbitrary superpositions of polynomial functions ...
Jun 2, 2021 · We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences.
Abstract. In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas se- quences. While the proofs of general statements rely on the ...
This work studies the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences.