有向根树上局部更新函数为NAND或NOR的广义并序动力系统的固定点
Fixed Points in Generalized Parallel Dynamical System with NAND or NOR Local Functions over Directed Rooted Trees
孙彦文 1郑洁1
作者信息
摘要
研究对象为有向根树上的广义并序动力系统,其局部更新函数为NAND或NOR.为了研究这类广义并序动力系统中的固定点的个数及状态,采用结构分析法和分类讨论法,得到了此类动力系统中关于固定点的确切结果.证明了这类广义并序动力系统中的固定点状态完全由有向根树中的自环决定.离散动力系统是数学建模的重要工具,该文可为离散动力系统的研究提供新的思路.
Abstract
In order to study the exact number and states of fixed points in the generalized dynamical system with NAND or NOR local functions over directed rooted trees,structural analysis and classification discussion methods are applied.The exact results of the fixed points in such dynamical systems are obtained.It is proved that the fixed points in such dynamical systems are completely determined by the loops in the rooted trees.This work provides a relevant advance in the knowledge of discrete dynamical systems which constitute mathematical tools to model simulation processes.
关键词
广义并序动力系统/有向根树/布尔函数/固定点Key words
generalized parallel dynamical system/directed rooted tree/Boolean function/fixed point引用本文复制引用
基金项目
2021 Shanghai Philosophy and Social Sciences Planning Project(2021BFX005)
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据