满射约束满足问题的代数全局装置
Algebraic Global Gadgetry for Surjective Constraint Satisfaction
AI总结：
提出了一个代数框架，通过计算全局装置将经典 CSP 归约到满射 CSP，统一证明了包括断开割、无彩虹 3-着色及 2-元素结构在内的多项满射 CSP 难度结果。
摘要：
有限关系结构 B 上的约束满足问题（CSP）是：给定一组变量上的约束（其关系来自 B），判断是否存在一个满足所有约束的变量赋值；满射 CSP 是其变体，即判断是否存在一个满射到 B 的论域上的满足赋值。我们提出了一个代数框架，用于证明满射 CSP 的难度结果；本质上，该框架计算全局装置，使得人们能够将经典 CSP 归约到满射 CSP。我们展示了如何在此框架下推导出满射 CSP 的一系列难度结果，包括断开割问题、无彩虹 3-着色问题，以及已知（在此设定下）难解的所有 2-元素结构上的满射 CSP 的难度。因此，我们的框架允许我们统一这些难度结果，并揭示它们之间的共同结构；我们相信，我们对断开割问题的难度证明比原始证明更为简洁。在我们看来，该框架也使得经典 CSP 如何归约到满射 CSP 的方式变得非常透明。
英文摘要：
The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B. We present an algebraic framework for proving hardness results on surjective CSPs; essentially, this framework computes global gadgetry that permits one to present a reduction from a classical CSP to a surjective CSP. We show how to derive a number of hardness results for surjective CSP in this framework, including the hardness of the disconnected cut problem, of the no-rainbow 3-coloring problem, and of the surjective CSP on all 2-element structures known to be intractable (in this setting). Our framework thus allows us to unify these hardness results, and reveal common structure among them; we believe that our hardness proof for the disconnected cut problem is more succinct than the original. In our view, the framework also makes very transparent a way in which classical CSPs can be reduced to surjective CSPs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
