Necessity of plurimorphisms versus sufficiency of polymorphisms

Ascertain whether computational complexity in the valued PCSP framework is fully determined by polymorphisms alone or whether plurimorphisms strictly add expressive power; either establish equivalence or produce a separating example.

Background

The paper’s reductions rely on plurimorphisms (finite families of weightings) rather than single polymorphisms, raising the question of necessity. If polymorphisms suffice, the theory could be simplified; if not, identifying minimal additional information needed would be crucial.

Resolving this will shape the algebraic foundation and the kinds of homomorphism tools required for classification results.