有限域在动力系统和逆向工程问题中的应用
Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems
摘要：
我们提出了一个数学模型：有限集上的动力系统（DSF），我们证明了布尔和离散遗传模型是DFS的特殊情况。本文证明了定义在不同元素个数的有限集上的函数可以表示为有限域上的多项式函数。给定定义在不同有限集上的函数的数据，我们描述了一种算法来获得与此数据相关联的所有多项式函数。因此，在调节网络中定义的所有函数都可以表示为有限域上的一个变量或多个变量的多项式函数。我们应用这些结果来研究逆向工程问题。
英文摘要：
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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