Parameterized complexity of weighted team definability

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2024-02-20 DOI:10.1017/s0960129524000033

Juha Kontinen, Yasir Mahmood, Arne Meier, Heribert Vollmer

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引用次数: 0

Abstract

In this article, we study the complexity of weighted team definability for logics with team semantics. This problem is a natural analog of one of the most studied problems in parameterized complexity, the notion of weighted Fagin-definability, which is formulated in terms of satisfaction of first-order formulas with free relation variables. We focus on the parameterized complexity of weighted team definability for a fixed formula

$\varphi$

of central team-based logics. Given a first-order structure

$\mathcal{A}$

and the parameter value

$k\in \mathbb N$

as input, the question is to determine whether

$\mathcal{A},T\models \varphi$

for some team T of size k. We show several results on the complexity of this problem for dependence, independence, and inclusion logic formulas. Moreover, we also relate the complexity of weighted team definability to the complexity classes in the well-known W-hierarchy as well as paraNP.

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加权团队可定义性的参数化复杂性

本文研究了具有团队语义的逻辑的加权团队可定义性的复杂性。这个问题是参数化复杂性中研究得最多的问题之一--加权法金可定义性概念--的自然类比，它是用具有自由关系变量的一阶公式的满足度来表述的。我们重点研究基于中心团队逻辑的固定公式 $\varphi$ 的加权团队可定义性的参数化复杂度。给定一阶结构 $\mathcal{A}$ 和参数值 $k\in \mathbb N$ 作为输入，问题是确定 $\mathcal{A},T 是否为某个大小为 k 的团队 T 的 \varphi$ 模型。此外，我们还将加权团队可定义性的复杂性与众所周知的 W-层次结构中的复杂性类别以及 paraNP 联系起来。

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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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.