$\Pi_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem

Dmitriy Zhuk

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arXiv · 2404.03844

$\Pi_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem

Dmitriy Zhuk

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Abstract

The Quantified Constraint Satisfaction Problem is the problem of evaluating a sentence with both quantifiers, over relations from some constraint language, with conjunction as the only connective. We show that for any constraint language on a finite domain the Quantified Constraint Satisfaction Problem is either in $\Pi_{2}^{P}$, or PSpace-complete. Additionally, we build a constraint language on a 6-element domain such that the Quantified Constraint Satisfaction Problem over this language is $\Pi_{2}^{P}$-complete.

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Dmitriy Zhuk. 2024-04-05. $\Pi_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem. https://arxiv.org/abs/2404.03844

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