约束满足的量子方法

Soichiro Fujii, Yuni Iwamasa, Kei Kimura
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引用次数: 1

摘要

约束满足问题(CSP)是一个包含了计算机科学中一系列重要问题的计算问题。我们指出CSP的基本概念,如实例的解集和多态,可以在有限集合和它们之间的函数集合的2范畴P FinSet中抽象地表述。2类P FinSet是一个量子类,其公式主要依赖于任何量子类中可用的结构。这一观察结果表明,CSP的推广和伴随的多态概念在一大类量子类中的正式发展。我们提取了一类优化问题作为特例,并证明了它们的计算复杂度可以通过相关的多态概念进行分类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Quantaloidal approach to constraint satisfaction
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 P FinSet of finite sets and sets of functions between them. The 2-category P FinSet 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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