A dichotomy theorem is established that splits the exponential case of Riis’s complexity gap theorem into two subcases, one that admits proofs of size f(k)nO(1) and one that does not and how the set of parameterized contradictions may be embedded into theSet of (ordinary) contradictions by the addition of new axioms.Expand

This work introduces surjective hyper-endomorphisms and uses them in proving a Galois connection that characterises definability in positive equality-free FO.Expand

The complexity of the quantified H-colouring problem is investigated using a new two player colouring game and it is conjecture that the last case extends to all non-bipartite connected graphs.Expand

It is proved that every discrete temporal CSP is in P or NP-complete, unless it can be formulated as a finite domain CSP, in which case the computational complexity is not known in general.Expand

Previous results on containment, equivalence and "coreness" for QCSP are recalled and extended before initiating a preliminary study of cores for QC SP which turns out to be more elusive.Expand

I present a survey of recent advances in the algorithmic and computational complexity theory of non-Boolean Quantified Constraint Satisfaction Problems, incorporating some more modern research… Expand