The Shortest Feedback Shift Register That Can Generate A Given Sequence
The Shortest Feedback Shift Register That Can Generate A Given Sequence
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DOI：
10.1007/0-387-34805-0_10
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发表时间：
1989-08
期刊：
影响因子：
--
通讯作者：
Cees J. A. Jansen;D. Boekee
中科院分区：
文献类型：
--
作者：
Cees J. A. Jansen;D. Boekee
在本文中，考虑了寻找绝对最短（可能是非线性）反馈移位寄存器的问题，该寄存器可以生成带有来自任意有限字母表的字符的给定序列。为此，定义了一种新的复杂性度量，称为最大阶复杂性。提出了一种新的非线性反馈移位寄存器理论，涉及转置序列和倒数序列的基本复杂性特性以及最大阶反馈移位寄存器等效的反馈函数。此外，Blumer 算法被认为是确定线性时间和内存中序列的最大阶复杂度概况及其周期的强大工具。显示了最大阶复杂度分布的典型行为，并讨论了给定序列分析和反馈移位寄存器综合的结果。
In this paper the problem of finding the absolutely shortest (possibly nonlin- ear) feedback shift register, which can generate a given sequence with characters from some arbitrary finite alphabet, is considered. To this end, a new complex- ity measure is defined, called the maximum order complexity. A new theory of the nonlinear feedback shift register is developed, concerning elementary complexity properties of transposed and reciprocal sequences, and feedback functions of the maximum order feedback shift register equivalent. Moreover, Blumer’s algorithm is identified as a powerful tool for determining the maxi- mum order complexity profile of sequences, as well as their period, in linear time and memory. The typical behaviour of the maximum order complexity profile is shown and the consequences for the analysis of given sequences and the synthesis of feedback shift registers are discussed.