COMPUTABILITY WITH LOW-DIMENSIONAL DYNAMICAL-SYSTEMS

被引：81

作者：

KOIRAN, P ^{[1
]}

COSNARD, M ^{[1
]}

GARZON, M ^{[1
]}

机构：

[1] MEMPHIS STATE UNIV,DEPT MATH SCI,MEMPHIS,TN 38152

来源：

THEORETICAL COMPUTER SCIENCE | 1994年 / 132卷 / 1-2期

关键词：

D O I：

10.1016/0304-3975(94)90229-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

It has been known for a short time that a class of recurrent neural networks has universal computational abilities. These networks can be viewed as iterated piecewise-linear maps in a high-dimensional space. In this paper, we show that similar systems in dimension two are also capable of universal computations. On the contrary, it is necessary to resort to more complex systems (e.g., iterated piecewise-monotone maps) in order to retain this capability in dimension one.

引用

页码：113 / 128

页数：16

共 17 条

[1] ON A THEORY OF COMPUTATION AND COMPLEXITY OVER THE REAL NUMBERS - NP-COMPLETENESS, RECURSIVE FUNCTIONS AND UNIVERSAL MACHINES [J].