On the Properties of T-functions with Uniform Differentiability

WANG Sen-peng; LIU Yan; HU Bin

doi:10.3969/j.issn.0372-2112.2016.11.016

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On the Properties of T-functions with Uniform Differentiability

更新时间：2025-07-16

- On the Properties of T-functions with Uniform Differentiability
- Acta Electronica Sinica Vol. 44, Issue 11, Pages: 2676-2681(2016)
- 作者机构：
  
  解放军信息工程大学,河南,郑州,450001
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61272041, No.61502532)
- DOI：10.3969/j.issn.0372-2112.2016.11.016
  CLC： TN918.1
- Published Online：25 November 2016，
  
  Published：2016
- 稿件说明：
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WANG Sen-peng, LIU Yan, HU Bin. On the Properties of T-functions with Uniform Differentiability[J]. Acta Electronica Sinica, 2016, 44(11): 2676-2681.
DOI：

WANG Sen-peng, LIU Yan, HU Bin. On the Properties of T-functions with Uniform Differentiability[J]. Acta Electronica Sinica, 2016, 44(11): 2676-2681. DOI： 10.3969/j.issn.0372-2112.2016.11.016.

摘要

本文结合传统T函数理论与非阿基米德T函数理论，深入研究T函数的性质特点，重点讨论一致可微T函数的单圈性及最高位序列的保熵性.首次利用参数的概念建立传统T函数理论中单字T函数单圈性判定条件与非阿基米德T函数理论中单圈性判定条件的联系，说明了两类判定条件的适用范围.定义了对T函数生成序列进行压缩变换的保熵性概念，讨论了一致可微T函数最高位序列的保熵性，说明了一致可微的T函数保熵性具有传递性，给出了T函数最高位序列保熵性的判定条件.

Abstract

Combining conventional theory with non-Archimedean theory

we study the properties of T-functions.We focus on the criteria of single cycle T-functions and entropy preservability of the most significant bit output sequence generated by T-functions.Utilizing the parameters

the connection between criteria of single cycle T-functions in two different theories is established.The situation each criterion is suited for is cleared.On the other hand

we define the notion of entropy preservability of T-functions.We talk about the entropy preservability of most significant bit output sequences generated by T-functions with uniform differentiability.We present the condition for entropy preservability of most significant bit output sequences and show the transitivity.

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