Computational complexity of general promise constraint satisfaction problems

Determine the computational complexity of general promise constraint satisfaction problems (PCSPs), including whether they admit a comprehensive complexity classification.

Background

Promise constraint satisfaction problems generalize constraint satisfaction problems by asking whether an input instance maps to a smaller structure or fails to map to a larger structure, under the promise that one of these alternatives holds. The paper studies the more specialized setting of promise systems of equations over finite algebras and establishes dichotomy results for several algebraic classes. It identifies the broader complexity theory of unrestricted PCSPs as unresolved, motivating the study of tractable and hard cases in structured settings.