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

TL;DR

This paper simplifies and generalizes the reduction of the Quantified CSP to the CSP for languages with the Polynomially Generated Powers property, enabling a complete complexity classification without the need for constants.

Contribution

It provides a simplified, generalized reduction method for QCSPs with PGP property, extending applicability to languages without constants and classifying their complexity.

Findings

Complete complexity classification for QCSP with PGP property

Simplified reduction applicable to languages without constants

Extended understanding of the complexity landscape of QCSPs

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.