Applications of finite fields to dynamical systems and reverse engineering problems

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.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS
      G.2.3 Applications

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.2 Design Tools and Techniques

Keywords:
dynamical systems, finite fields, partially defined functions, regulatory networks