An Algorithmic Characterization of Polynomial Functions over Z_{p^n}

Details An Algorithmic Characterization of Polynomial Functions over Z_{p^n} An Algorithmic Characterization of Polynomial Functions over Z_{p^n}

2012-03-06

arxiv.org/abs/1203.1122v1

Computer Science

Symbolic Computation

Scientific paper

In this paper we consider polynomial representability of functions defined over Z_{p^n}, where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that answers the decision problem: to determine whether a given function over Z_{p^n} is polynomially representable or not. The previous characterizations given by Carlitz (1964) and Kempner (1921) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. We present a new characterization which leads to an algorithm whose running time is linear in size of input.

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