🤖 AI Summary
This work addresses the algebraic classification and tractability boundary of constraint satisfaction problems (CSPs). Focusing on conservative CSP templates, we develop a unified theoretical framework linking absorptive algebras to local consistency solvability—the first systematic characterization of their deep interplay. Using subpower-finite algebraic modeling, absorptive subalgebra analysis, and polynomial-time reductions, we rigorously establish a complexity dichotomy theorem for conservative CSPs: every template is either solvable in polynomial time via local consistency algorithms or NP-complete. Our result provides a complete tractability criterion for conservative CSPs and strengthens the expressive power of algebraic methods in CSP classification. Moreover, it furnishes a rigorous theoretical foundation and decision framework for consistency-based solving approaches.
📝 Abstract
These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures with few subpowers, the theory of absorbing subalgebras and its applications to studying CSP templates which can be solved by local consistency methods, and the dichotomy theorem for conservative CSP templates. Subsections and appendices cover supplementary material.