Quantaloidal Approach to Constraint Satisfaction

Soichiro Fujii
Yuni Iwamasa
Kei Kimura

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.

In Kohei Kishida: Proceedings of the Fourth International Conference on Applied Category Theory (ACT 2021), Cambridge, United Kingdom, 12-16th July 2021, Electronic Proceedings in Theoretical Computer Science 372, pp. 289–305.
Published: 3rd November 2022.

ArXived at: http://dx.doi.org/10.4204/EPTCS.372.21 bibtex PDF
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