论文标题
两个离散动力学模型的关系：一维蜂窝自动机和积分值转换
Relationship of Two Discrete Dynamical Models: One-dimensional Cellular Automata and Integral Value Transformations
论文作者
论文摘要
蜂窝自动机（CA）和积分值转换（IVT）是两个已建立的数学模型，它们会在离散的时间步骤中演变。从理论上讲，对CA的研究表明CA能够产生各种进化模式。但是，非线性CA或更高维CA的计算可能很复杂，而IVT可以轻松操纵。本文的主要目的是研究一维CA和IVT的过渡函数之间的联系。从数学上讲，我们还建立了使用二进制操作的一维CA以及一组IVT的一组过渡函数的代数结构。也使用IVT对DNA序列进化进行了建模。
Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of evolution patterns. However computation of non-linear CA or higher dimensional CA maybe complex, whereas IVTs can be manipulated easily. The main purpose of this paper is to study the link between a transition function of a one-dimensional CA and IVTs. Mathematically, we have also established the algebraic structures of a set of transition functions of a one-dimensional CA as well as that of a set of IVTs using binary operations. Also DNA sequence evolution has been modelled using IVTs.
