Promise Constraint Satisfaction and Width

This lecture covers the complexity of Promise Constraint Satisfaction Problems (PCSPs) and their width, including topics such as approximate graph coloring, complexity classes, local consistency algorithms, polymorphisms, and reductions. The instructor presents results on the Barto-Kozik Theorem, weak near unanimity operations, and the implications of sublinear width in PCSPs. The lecture also explores the use of sparse random hypergraphs, boundary exploitation, and the implications of unsatisfiable subinstances. Additionally, it discusses the implications of bounded width in PCSPs and the development of new algorithms for solving specific PCSP instances.