有序半群的特征,产生良好的词准有序半群

IF 0.6 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
Ondřej Klíma, Jonatan Kolegar
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引用次数: 0

摘要

由所有词的半群到有限有序半群的同构所产生的准序概念是由布歇等人提出的(《计算科学理论》,40, 131-148 1985 年)。他们在研究与一组给定的无上下文规则相关联的派生关系时自然而然地提出了一个关键问题:由此产生的关系是否是一个良好的准有序关系。我们以半群同态生成的准序为例来回答这个问题。我们证明,答案并不取决于同态,而是其映像的属性。此外,我们还给出了得到良好准阶的有限半群的代数特征。这一表征完善了昆奇 (Theor. Comput. Sci. 348, 277-293 2005) 在等价有序半群情况下给出的结构表征。与昆奇的表征相比,新表征在结构上没有任何意义,我们将解释其原因。此外,我们还证明了新条件可在多项式时间内检验。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words

The notion of a quasi-order generated by a homomorphism from the semigroup of all words onto a finite ordered semigroup was introduced by Bucher et al. (Theor. Comput. Sci. 40, 131–148 1985). It naturally occurred in their studies of derivation relations associated with a given set of context-free rules, and they asked a crucial question, whether the resulting relation is a well quasi-order. We answer this question in the case of the quasi-order generated by a semigroup homomorphism. We show that the answer does not depend on the homomorphism, but it is a property of its image. Moreover, we give an algebraic characterization of those finite semigroups for which we get well quasi-orders. This characterization completes the structural characterization given by Kunc (Theor. Comput. Sci. 348, 277–293 2005) in the case of semigroups ordered by equality. Compared with Kunc’s characterization, the new one has no structural meaning, and we explain why that is so. In addition, we prove that the new condition is testable in polynomial time.

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来源期刊
Theory of Computing Systems
Theory of Computing Systems 工程技术-计算机:理论方法
CiteScore
1.90
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: TOCS is devoted to publishing original research from all areas of theoretical computer science, ranging from foundational areas such as computational complexity, to fundamental areas such as algorithms and data structures, to focused areas such as parallel and distributed algorithms and architectures.
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