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Network satisfaction for symmetric relation algebras with a flexible atom
arXiv - CS - Computational Complexity Pub Date : 2020-08-27 , DOI: arxiv-2008.11943
Manuel Bodirsky and Simon Kn\"auer

Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras $\bf A$. We provide a complete classification for the case that $\bf A$ is symmetric and has a flexible atom; the problem is in this case NP-complete or in P. If a finite integral relation algebra has a flexible atom, then it has a normal representation $\mathfrak{B}$. We can then study the computational complexity of the network satisfaction problem of ${\bf A}$ using the universal-algebraic approach, via an analysis of the polymorphisms of $\mathfrak{B}$. We also use a Ramsey-type result of Ne\v{s}et\v{r}il and R\"odl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.

中文翻译:

具有灵活原子的对称关系代数的网络满意度

Robin Hirsch 在 1996 年提出了真正的大复杂性问题:对所有有限关系代数 $\bf A$ 的网络满意度问题的计算复杂性进行分类。我们对 $\bf A$ 对称且具有柔性原子的情况提供了完整的分类;问题在这种情况下是 NP 完全的或在 P 中。如果有限积分关系代数有一个灵活的原子,那么它有一个正规的表示 $\mathfrak{B}$。然后,我们可以通过对 $\mathfrak{B}$ 的多态性的分析,使用通用代数方法研究 ${\bf A}$ 的网络满意度问题的计算复杂度。我们还使用 Ne\v{s}et\v{r}il 和 R\"odl 的 Ramsey 型结果以及 Bulatov 的复杂性二分法结果来解决保守的有限域约束满足问题。
更新日期:2020-08-28
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