Partial Polymorphisms and Constraint Satisfaction Problems

The Galois connection between clones and and co-clones has received a lot of attention in the context of complexity considerations for constraint satisfaction problems. However, it fails if we are interested in a reduction giving equivalence instead of only satisfiability-equivalence. We show how a similar Galois connection involving weaker closure operators can be applied for these problems. As an example of the usefulness of our construction, we show how to obtain very short proofs of complexity classifications in this context.

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