TREE EXPRESSIONS AND THEIR PRODUCT FORMULA
Shuichi Inokuchi, Yasuo Kawahara · Bulletin of informatics and cybernetics · 2003
In this paper we propose tree expressions which express transition diagrams of finite dynamical systems by algebraic formula. And we consider the cartesian product of dynamical systems and get the product formula of tree expressions. By the product formula we easily get the tree expression of the product of dynamical systems represented by tree expressions. Keywords : Tree Expression, Product Formula, Dynamical System 1 Introduction In nature there exist many natural dynamical systems and many researchers investigate them. Many artificial dynamical systems are devised by engineers and scientists. They investigate dynamical systems and applied them to many fields. Generally dynamical systems are represented by a pair (X; f) of an non empty set X and a transition function f on X. It is difficult to understand behaviors of a dynamical system (X; f ). So in order to understand behaviors of dynamical systems more easily we describe their transition diagrams which are graphs showing their t...