通过多态性研究纠缠图染色的复杂性
The complexity of entangled graph colouring via polymorphisms
浏览论文内容
中文总结 AI 辅助
本文通过将多态性归约推广至纠缠CSP，证明了超过三种颜色的纠缠图染色问题的不可判定性。
中文摘要 AI 辅助
具有算子赋值的约束满足问题（CSP）为研究非局部博弈类的纠缠值的判定复杂性提供了一个结构良好的框架。由于CSP二分定理，经典赋值下约束满足问题的复杂性可以通过研究CSP的对称性（即底层关系结构的多态性）来完全理解。在本工作中，我们证明基于多态性的CSP之间的归约可以推广为基于纠缠多态性模拟的纠缠CSP之间的间隙保持归约。这一归约使我们能够证明超过三种颜色的纠缠图染色问题的不可判定性，而该问题此前已被证明对基于交换性小工具的硬度归约具有抵抗性。
英文摘要
Constraint satisfaction problems (CSPs) with operator assignments to the variables provide a well-structured setting to study the decision complexity of the entangled value of classes of nonlocal games. Due to the CSP dichotomy theorem, the complexity of constraint satisfaction problems with classical assignments can be fully understood by studying the symmetries of the CSP, in terms of the polymorphisms of the underlying relational structure. In this work, we show that the polymorphism-based reductions between CSPs can be generalised to gap-preserving reductions between entangled CSPs based on an entangled analogue of the polymorphisms. This reduction allows us to show undecidability of entangled graph colouring with more than three colours, a problem that has proved resistant to prior hardness reductions based on commutativity gadgets.
