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On polynomial recursive sequences (2002.08630v1)
Published 20 Feb 2020 in cs.FL
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.