线性数据集与关系结构的有界路对偶
Linear Datalog and Bounded Path Duality of Relational Structures
摘要：
本文系统地研究了有限变量逻辑、有界路宽结构和线性数据库程序之间的联系。我们证明，在约束满足问题的背景下，所有这些概念对应于一个独特的强大的概念，我们称之为有界路径对偶不同的数学体现。我们还研究了有界路径对偶概念的计算复杂性含义。我们表明，每一个约束满足问题$\csp(\best)$与有界路径对偶是可解的NL，这一概念解释了在一个统一的方式所有家庭的CSP已知在NL。最后，我们使用的结果在文件中确定NL中的新问题。
英文摘要：
In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems, all these concepts correspond to different mathematical embodiments of a unique robust notion that we call bounded path duality. We also study the computational complexity implications of the notion of bounded path duality. We show that every constraint satisfaction problem $\csp(\best)$ with bounded path duality is solvable in NL and that this notion explains in a uniform way all families of CSPs known to be in NL. Finally, we use the results developed in the paper to identify new problems in NL.
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