  We present a mathematical model: dynamical systems over finite sets (DSF),
and we show that Boolean and discrete genetic models are special cases of DFS.
In this paper, we prove that a function defined over finite sets with different
number of elements can be represented as a polynomial function over a finite
field. Given the data of a function defined over different finite sets, we
describe an algorithm to obtain all the polynomial functions associated to this
data. As a consequence, all the functions defined in a regulatory network can
be represented as a polynomial function in one variable or in several variables
over a finite field. We apply these results to study the reverse engineering
problem.
