The complexity of the Quantified CSP having the polynomially generated powers property

Abstract: It is known that if an algebra of polymorphisms of the constraint language has the Polynomially Generated Powers (PGP) Property then the Quantified CSP can be reduced to the CSP over the same constraint language with constants. The only limitation of this reduction is that it is applicable only for the constraint languages with constants. We drastically simplified the reduction and generalized it for constraint languages without constants. As a result, we completely classified the complexity of the QCSP for constraint languages having the PGP property.