We consider constraint satisfaction problems parameterized by the set of allowed constraint predicates. We examine the complexity of quantified constraint satisfaction problems with a bounded number of quantifier alternations and the complexity of the associated counting problems. We obtain classification results that completely solve the Boolean case, and we show ... more >>>

Quantified constraint satisfaction is the generalization of
constraint satisfaction that allows for both universal and existential
quantifiers over constrained variables, instead
of just existential quantifiers.
We study quantified constraint satisfaction problems ${\rm CSP}(Q,S)$, where $Q$ denotes
a pattern of quantifier alternation ending in exists or the set of all possible
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