约束满足的量子化方法
Quantaloidal Approach to Constraint Satisfaction
摘要：
约束满足问题（CSP）是一个计算问题，它包含了计算机科学中的一系列重要问题。我们指出，CSP的基本概念，如一个实例的解决方案集和多态性，可以制定抽象内的2类PFinSet的有限集和它们之间的功能集。2类PFinSet是一个quantaloid，其公式主要依赖于任何quantaloid中可用的结构。这一观察结果表明，一个正式的发展概括的CSP和随之而来的概念，多态性的一大类quantaloids。我们提取一类优化问题作为特殊情况，并表明它们的计算复杂性可以通过相关的多态性概念来分类。
英文摘要：
The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and polymorphisms, can be formulated abstractly inside the 2-category PFinSet of finite sets and sets of functions between them. The 2-category PFinSet is a quantaloid, and the formulation relies mainly on structure available in any quantaloid. This observation suggests a formal development of generalisations of the CSP and concomitant notions of polymorphism in a large class of quantaloids. We extract a class of optimisation problems as a special case, and show that their computational complexity can be classified by the associated notion of polymorphism.
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