Fibonacci Word Lex-parse Sensitivity Analysis

Core Concepts

Lex-parse sensitivity to edit operations and alphabet ordering is analyzed using Fibonacci words, revealing tight upper and lower bounds.

Abstract

The content delves into the sensitivity analysis of lex-parse with respect to edit operations and alphabet ordering using Fibonacci words. The study provides insights into compression sensitivity and repetitiveness measures, showcasing the robustness of lex-parse. The analysis reveals tight upper and lower bounds for both edit operations and alphabet ordering sensitivity. Various structures and properties of strings, including Lyndon factorization and Fibonacci words, are explored to characterize the lex-parse structure.

1. Introduction

   • Dictionary compression effectiveness for repetitive text collections.
   • Sensitivity of compressors and repetitiveness measures.

2. Preliminaries

   • Definitions and properties of strings, prefixes, substrings, and suffixes.
   • Lyndon factorization and Fibonacci words.

3. Sensitivity of Lex-parse

   • Sensitivity to edit operations and alphabet ordering.
   • Analysis of compression sensitivity variants.

4. Upper Bounds

   • Tight upper bounds for edit operations and alphabet ordering sensitivity.

5. Lower Bounds for Edit Operations

   • Tight lower bounds using Fibonacci words.

6. Lower Bounds for Alphabet-Ordering

   • Tight lower bounds using Fibonacci words.

7. Acknowledgments

   • Support from JSPS KAKENHI Grant Numbers.

Stats

v(w2) ∈ O(b(w2) log(n/b(w2)))
v(w, ≺) ∈ O(b(w) log(n/b(w)))

Quotes

"The lex-parse of a string is a greedy left-to-right partitioning."
"Each phrase can be encoded by a pair (0, T[i]) or (ℓ, i′)."

Key Insights Distilled From

Edit and Alphabet-Ordering Sensitivity of Lex-parse

by Yuto... at arxiv.org 03-01-2024

https://arxiv.org/pdf/2402.19223.pdf

Deeper Inquiries

어떻게 lex-parse의 민감도가 다른 압축 측정 방법과 비교되는가?

lex-parse의 민감도는 Akagi 등이 제안한 다른 측정 방법들과 비교했을 때 상당히 효율적임을 보여줍니다. Akagi 등이 소개한 민감도 측정은 문자열의 작은 변경 또는 오류에 대한 압축기의 견고성을 나타내는데, lex-parse는 이러한 작은 변화에 대해 상당히 견고한 것으로 나타났습니다. 특히, lex-parse는 입력 텍스트의 길이에 로그함수적인 상한선과 하한선을 가지고 있어, 다른 측정 방법들과 비교했을 때 상당히 효율적인 압축 방법임을 보여줍니다.