Stringological sequence prediction III: layered ziplines and a tradeoff between efficiency and expressivity

2026-09-17

AI Summary

研究通过引入一种称为分层zipline程序的限制类，提出了一种与ARC相关的较弱复杂度度量，该方法在保证高效算法的同时牺牲了部分表达力。

Abstract

In previous papers, we began the study of sequence prediction algorithms adapted to stringological word complexity measures. In particular, we defined a complexity measure called Arithmetic Repetition Complexity (ARC) which admits a polynomial-time prediction algorithm with a mistake bound quasilinear in the complexity. Here, we show a weaker complexity measure related to ARC that admits an especially efficient prediction algorithm: an algorithm that runs in quasilinear time and polylog space for appropriate highly-structured sequences. The complexity measure is defined via a restricted class of "zipline programs" (a variant of straight-line programs), which we call layered. We thus get a less expressive measure with a more efficient algorithm (compared to our results for ARC), demonstrating a possible tradeoff.

Problem

• sequence prediction
• stringological complexity
• efficiency
• expressivity
• zipline programs

Innovation

• layered zipline programs
• quasilinear time
• polylog space
• efficiency and expressivity tradeoff