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It is known that if an algebra of polymorphisms of the constraint languagehas the Polynomially Generated Powers (PGP) Property then the Quantified CSPcan be reduced to the CSP over the same constraint language with constants. Theonly limitation of this reduction is that it is applicable only for theconstraint languages with constants. We drastically simplified the reductionand generalized it for constraint languages without constants. As a result, wecompletely classified the complexity of the QCSP for constraint languageshaving the PGP property.

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