The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems
We prove that an ω-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that this happens if and only if its polymorphism clone does not contain...
Uloženo v:
| Vydáno v: | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science s. 615 - 622 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
New York, NY, USA
ACM
05.07.2016
|
| Edice: | ACM Conferences |
| Témata: | |
| ISBN: | 9781450343916, 1450343910 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | We prove that an ω-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that this happens if and only if its polymorphism clone does not contain operations α, β, s satisfying the identity αs(x, y, x, z, y, z) ≈ βs(y, x, z, x, z, y).
This establishes an algebraic criterion equivalent to the conjectured borderline between P and NP-complete CSPs over reducts of finitely bounded homogenous structures, and accomplishes one of the steps of a proposed strategy for reducing the infinite domain CSP dichotomy conjecture to the finite case.
Our theorem is also of independent mathematical interest, characterizing a topological property of any ω-categorical core structure (the existence of a continuous homomorphism of a stabilizer of its polymorphism clone to the projections) in purely algebraic terms (the failure of an identity as above). |
|---|---|
| ISBN: | 9781450343916 1450343910 |
| DOI: | 10.1145/2933575.2934544 |