希格曼引理多集扩展的紧长度定理

IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Vitor Greati , Revantha Ramanayake
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引用次数: 0

摘要

一个良准有序(wqo)集合推广了良基础的概念,并且是通过控制坏序列的长度上界(称为长度定理)来分析计算问题复杂性的强大工具。wq -set的有限多集扩展在该集合的元素上推导出有限多集上的排序,其中一个多集先于另一个多集,如果它们的元素之间存在保持原始排序的内射映射。本文改进了有限字母上希格曼序的有限多集扩展的长度定理,并建立了一个匹配的下界。作为一个推论,我们得到了有限字母上希格曼序的主要扩展的更紧的长度界。我们证明了我们的结果在非交换超序列逻辑的复杂性分析中的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tight length theorems for multiset extensions of Higman’s lemma
A well-quasi-ordered (wqo) set generalizes the notion of well-foundedness and is a powerful tool for analyzing the complexity of computational problems through upper bounds on the length of controlled bad sequences, known as length theorems. The finitary multiset extension of a wqo-set induces an ordering on finite multisets over elements of that set, where one multiset precedes another if there exists an injective mapping between their elements that preserves the original ordering. In this work, we refine existing length theorems for the finitary multiset extension of Higman’s ordering over finite alphabets, and we establish a matching lower bound. As a corollary, we obtain tighter length bounds for the majoring extension of Higman’s ordering over finite alphabets. We demonstrate the application of our results in the complexity analysis of noncommutative hypersequent logics.
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来源期刊
Theoretical Computer Science
Theoretical Computer Science 工程技术-计算机:理论方法
CiteScore
2.60
自引率
18.20%
发文量
471
审稿时长
12.6 months
期刊介绍: Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
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