Random feedback shift registers and the limit distribution for largest cycle lengths

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Combinatorics, Probability & Computing Pub Date : 2023-02-14 DOI:10.1017/s0963548323000020

Richard Arratia, E. Rodney Canfield, Alfred W. Hales

引用次数: 0

Abstract

Abstract For a random binary noncoalescing feedback shift register of width $n$ , with all $2^{2^{n-1}}$ possible feedback functions $f$ equally likely, the process of long cycle lengths, scaled by dividing by $N=2^n$ , converges in distribution to the same Poisson–Dirichlet limit as holds for random permutations in $\mathcal{S}_N$ , with all $N!$ possible permutations equally likely. Such behaviour was conjectured by Golomb, Welch and Goldstein in 1959.

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随机反馈移位寄存器和最大周期长度的极限分布

摘要对于宽度为$n$的随机二元非聚结反馈移位寄存器，当所有$2^{2^{n-1}}$可能的反馈函数$f$等可能时，长周期长度的过程在分布上收敛于与$\mathcal{S}_N$中的随机排列相同的泊松-狄利克雷极限，且所有$n !$种可能的排列等可能。1959年，Golomb、Welch和Goldstein推测出了这种行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.

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