测量重复性的l系统

G. Navarro, Cristian Urbina
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引用次数: 0

摘要

L-system(用于无损压缩)是用两个参数$d$和$n$扩展的cpd0 -system,它明确地确定字符串$w = \tau(\varphi^d(s))[1:n]$,其中$\varphi$是系统的态射,$s$是它的公理,$\tau$是它的编码。生成$w$的l系统的最短描述的长度为$\ell$,并且可以说是建立在序列中出现的自相似性基础上的重复性的相关度量。在本文中,我们深入研究了测度$\ell$及其与$\delta$的关系,是一个建立在子串复杂度上的较好的下界。我们的结果表明$\ell$和$\delta$在很大程度上是正交的,在某种意义上,根据情况,一个可能比另一个大得多。这表明重复的两种来源在很大程度上是不相关的。我们还证明了最近引入的将l系统的能力与双向宏观方案相结合的nu -系统可以渐近严格小于这两种机制,这使得最小nu -系统的尺寸$\nu$成为迄今为止唯一的最小可达重复性度量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
L-systems for Measuring Repetitiveness
An L-system (for lossless compression) is a CPD0L-system extended with two parameters $d$ and $n$, which determines unambiguously a string $w = \tau(\varphi^d(s))[1:n]$, where $\varphi$ is the morphism of the system, $s$ is its axiom, and $\tau$ is its coding. The length of the shortest description of an L-system generating $w$ is known as $\ell$, and is arguably a relevant measure of repetitiveness that builds on the self-similarities that arise in the sequence. In this paper we deepen the study of the measure $\ell$ and its relation with $\delta$, a better established lower bound that builds on substring complexity. Our results show that $\ell$ and $\delta$ are largely orthogonal, in the sense that one can be much larger than the other depending on the case. This suggests that both sources of repetitiveness are mostly unrelated. We also show that the recently introduced NU-systems, which combine the capabilities of L-systems with bidirectional macro-schemes, can be asymptotically strictly smaller than both mechanisms, which makes the size $\nu$ of the smallest NU-system the unique smallest reachable repetitiveness measure to date.
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