Tractable Combinations of Temporal CSPs

M. Bodirsky, Johannes Greiner, Jakub Rydval
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引用次数: 1

Abstract

The constraint satisfaction problem (CSP) of a first-order theory $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. We study the computational complexity of $\mathrm{CSP}(T_1 \cup T_2)$ where $T_1$ and $T_2$ are theories with disjoint finite relational signatures. We prove that if $T_1$ and $T_2$ are the theories of temporal structures, i.e., structures where all relations have a first-order definition in $(\mathbb{Q};<)$, then $\mathrm{CSP}(T_1 \cup T_2)$ is in P or NP-complete. To this end we prove a purely algebraic statement about the structure of the lattice of locally closed clones over the domain ${\mathbb Q}$ that contain $\mathrm{Aut}(\mathbb{Q};<)$.
时间csp的可处理组合
一阶理论$T$的约束满足问题(CSP)是在$T$的某个模型中决定给定的原子公式的连接是否可满足的计算问题。研究了$\ mathm {CSP}(T_1 \cup T_2)$的计算复杂度,其中$T_1$和$T_2$是具有不相交有限关系签名的理论。我们证明了如果$T_1$和$T_2$是时间结构的理论,即所有关系在$(\mathbb{Q};<)$中有一阶定义的结构,则$\ mathm {CSP}(T_1 \cup T_2)$是P或np完全的。为此,我们证明了${\mathbb Q}$上包含$\ mathm {Aut}(\mathbb{Q};<)$的局部闭克隆的格结构的一个纯代数命题。
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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