带终极周期计数的两变量逻辑

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2024-07-08 DOI:10.1137/22m1504792

Michael Benedikt, Egor V. Kostylev, Tony Tan

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引用次数: 0

摘要

SIAM 计算期刊》，第 53 卷第 4 期，第 884-968 页，2024 年 8 月。摘要。我们考虑用量词对[math]进行扩展，量词表示公式成立的元素数应属于给定的最终周期集。我们证明该逻辑的可满足性和有限可满足性都是可判定的。我们还证明，任何句子的谱，即其有限模型的大小集合，都可以用普雷斯伯格算术来定义。在此过程中，我们提出了对 "双圆图方法 "的若干改进。在这种方法中，有关双变量逻辑的可判定性问题被简化为与分区图相关的整数向量的普雷斯伯格可定义性问题，其中分区中的节点满足其入度和出度的某些约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Two Variable Logic with Ultimately Periodic Counting

SIAM Journal on Computing, Volume 53, Issue 4, Page 884-968, August 2024.
Abstract. We consider the extension of [math] with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of the logic are decidable. We also show that the spectrum of any sentence, i.e., the set of the sizes of its finite models, is definable in Presburger arithmetic. In the process we present several refinements to the “biregular graph method.” In this method, decidability issues concerning two-variable logics are reduced to questions about Presburger definability of integer vectors associated with partitioned graphs, where nodes in a partition satisfy certain constraints on their in- and out-degrees.

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来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.