Π_2^P vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem
arxiv(2024)
摘要
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 Π_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 Π_2^P-complete.
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