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.

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关于多项式递归序列

我们研究多项式递归序列的表达能力，这是众所周知的线性递归序列类的非线性扩展。这些序列在加权自动机的非线性扩展研究中自然出现，其中（非）表达性结果转化为类分离。多项式递归序列的典型示例是b _n = n !。我们的主要结果是序列u _n = n ⁿ不是多项式递归。