Maltsev + Datalog --≫ Symmetric Datalog

Abstract

Let B be a finite, core relational structure and let A be the algebra associated to B, i.e. whose terms are the operations on the universe of B that preserve the relations of B. We show that if A generates a so-called arithmetical variety then CSP(B), the constraint satisfaction problem associated to B, is solvable in Logspace; in fact notCSP(B) is expressible in symmetric Datalog. In particular, we obtain that notCSP(B) is expressible in Datalog and the relations of B are invariant under a Maltsev operation then notCSP(B) is in symmetric Datalog.