加权团队可定义性的参数化复杂性
Parameterized Complexity of Weighted Team Definability
摘要：
在这篇文章中，我们研究的复杂性加权团队可定义的逻辑与团队语义。这个问题是一个自然的模拟研究最多的问题之一，参数化的复杂性，加权Fagin定义的概念，这是制定在满足一阶公式与自由关系变量。我们专注于加权团队可定义性的参数化复杂性为一个固定的公式φ的中心团队为基础的逻辑。给定一个一阶结构A和参数值k作为输入，问题是确定A，T是否为某个规模为k的团队T建模phi。我们展示了几个结果，这个问题的依赖，独立和包含逻辑公式的复杂性。此外，我们还与加权团队定义的复杂性，在著名的W-层次结构以及paraNP的复杂性类。
英文摘要：
In this article, we study the complexity of weighted team definability for logics with team semantics. This problem is a natural analogue 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 phi of central team-based logics. Given a first-order structure A and the parameter value k as input, the question is to determine whether A,T models phi 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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