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Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems

Maria A. Avino-Diaz·Edward Green·Oscar Moreno
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Abstract

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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BibTeXRIS

Maria A. Avino-Diaz, Edward Green, Oscar Moreno. 2006-03-15. Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems. https://arxiv.org/abs/math/0603369

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