Let \(R\) be a finite, commutative, unital ring. A polynomial \(p\in R[x]\) naturally induces a function \(p_f:R\rightarrow R\) by substitution. A function \(f:R\rightarrow R\) is a polynomial function if there exists a polynomial \(p_f\in R[x]\) such that \(p_f(r) = f(r)\) for every \(r\in R\). A ring is local if it has a unique maximal ideal. As is well known every finite commutative, unital ring is a direct sum of local rings. So it is enough to consider finite, commutative, unital, local rings. The Authors of this paper gave a necessary and sufficient condition for a function being a polynomial function over a finite, commutative, unital ring. Furthermore, they gave an algorithm running in quasilinear time that determines whether or not a function given by its function table can be represented by a polynomial, and if the answer is yes then it provides one such polynomial.