Relaxations for the constraint satisfaction problem (CSP) include bounded width, linear program (LP), semidefinite program (SDP), afinfe integer program (AIP), and the combined LP+AIP of Brakensiek, Guruswami, Wrochna, and Živný (SICOMP 2020). Tightening relaxations systematically leads to hierarchies and stronger algorithms. For the LP+AIP hierarchy, a constant level lower bound ... more >>>

We show optimal (up to constant factor) NP-hardness for Max-k-CSP over any domain,
whenever k is larger than the domain size. This follows from our main result concerning predicates
over abelian groups. We show that a predicate is approximation resistant if it contains a subgroup that
is ... more >>>