Applications of finite fields to dynamical systems and reverse engineering problems

Authors:
María A. Aviñó;Edward Green;Oscar Moreno
Affiliations:
University of Puerto Rico at Cayey Cayey, PR;Virginia Tech, Blacksburg, VA;University of Puerto Rico at Rio Piedras, Rio Piedras, PR
Venue:
Proceedings of the 2004 ACM symposium on Applied computing
Year:
2004

Citing 3
Cited 0

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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, [1, 4, 10].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.