Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems

Details Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems

2006-03-15

arxiv.org/abs/math/0603369v1

2004 ACM Symposium on Applied Computing, SAC04, Nicosia, Chipre

Mathematics

Dynamical Systems

Scientific paper

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.

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