A Faster Algorithm For Testing Polynomial Representability Of Functions   Over Finite Integer Rings
  Given a function from $\mathbb{Z}_n$ to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over $\mathbb{Z}_n$ by constructing a generating set for the $\mathbb{Z}_{n}$-module of polynomial functions. This characterization results in an algorithm that is faster on average in deciding polynomial representability. We also extend the characterization to functions in several variables. 
Ashwin Guha, Ambedkar Dukkipati
math.RA