5 research outputs found
QCSP monsters and the demise of the chen conjecture.
We give a surprising classification for the computational complexity
of the Quantified Constraint Satisfaction Problem over a constraint
language Γ, QCSP(Γ), where Γ is a finite language over 3 elements
which contains all constants. In particular, such problems are either in P, NP-complete, co-NP-complete or PSpace-complete. Our
classification refutes the hitherto widely-believed Chen Conjecture.
Additionally, we show that already on a 4-element domain there
exists a constraint language Γ such that QCSP(Γ) is DP-complete
(from Boolean Hierarchy), and on a 10-element domain there exists
a constraint language giving the complexity class Θ
????
2
.
Meanwhile, we prove the Chen Conjecture for finite conservative languages Γ. If the polymorphism clone of such Γ has the
polynomially generated powers (PGP) property then QCSP(Γ) is in
NP. Otherwise, the polymorphism clone of Γ has the exponentially
generated powers (EGP) property and QCSP(Γ) is PSpace-complete
QCSP on reflexive tournaments
We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well known that reflexive tournaments can be split into a sequence of strongly connected components H1,…,Hn so that there exists an edge from every vertex of Hi to every vertex of Hj if and only if
QCSP monsters and the demise of the chen conjecture
We give a surprising classification for the computational complexity of the Quantified Constraint Satisfaction Problem over a constraint language Γ, QCSP(Γ), where Γ is a finite language over 3 elements which contains all constants. In particular, such problems are either in P, NP-complete, co-NP-complete or PSpace-complete. Our classification refutes the hitherto widely-believed Chen Conjecture. Additionally, we show that already on a 4-element domain there exists a constraint language Γ such that QCSP(Γ) is DP-complete (from Boolean Hierarchy), and on a 10-element domain there exists a constraint language giving the complexity class Θ ???? 2 . Meanwhile, we prove the Chen Conjecture for finite conservative languages Γ. If the polymorphism clone of such Γ has the polynomially generated powers (PGP) property then QCSP(Γ) is in NP. Otherwise, the polymorphism clone of Γ has the exponentially generated powers (EGP) property and QCSP(Γ) is PSpace-complete