Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between polynomial-time tractability and NP-hardness. In this course we introduce the universal-algebraic approach to study the computational complexity of finite-domain CSPs. The course covers in particular the cyclic terms and bounded width theorems. To keep the presentation accessible, we start the course in the tangible setting of directed graphs and graph homomorphism problems.

翻译：约束满足问题是一类在理论计算机科学多个领域自然出现的计算问题。其核心研究主题之一是计算复杂性，特别是多项式时间可解性与NP困难性之间的边界。本课程介绍研究有限域约束满足问题计算复杂性的泛代数方法，重点涵盖循环项定理与有界宽度定理。为使内容易于理解，我们从有向图与图同态问题的具体背景切入展开论述。