Weisfeiler-Leman Invariant Promise Valued CSPs

Algebraic Approach to Approximation

“…Output yes if Φ A ≠ ∅; no if Φ B = ∅. 5 In this context, 𝑋 is regarded as a set of variables and the 𝜏-sorted functions ℎ : 𝑋 → 𝐴 as assignments of values in 𝐴 to variables. The fact that 𝜙 A 𝑖 (ℎx 𝑖 ) means that the constraint 𝜙 𝑖 (x 𝑖 ) is satisfied in A by the assignment ℎ.…”

“…It includes, as special cases, (non-valued) PCSPs (and thus also CSPs), valued CSPs, approximation of CSPs (both constant factor and gap variants), Gap Label Cover, and Unique Games. The only previous works on valued PCSPs are the algorithmic results in [5,53] and the unpublished manuscript of Kazda developing an algebraic theory for constant factor approximation of valued PCSPs [38], cf. Appendix D.…”