2022
DOI: 10.1137/20m1383471
|View full text |Cite
|
Sign up to set email alerts
|

When Symmetries Are Not Enough: A Hierarchy of Hard Constraint Satisfaction Problems

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

0
6
0

Year Published

2022
2022
2024
2024

Publication Types

Select...
7
1

Relationship

1
7

Authors

Journals

citations
Cited by 9 publications
(6 citation statements)
references
References 23 publications
0
6
0
Order By: Relevance
“…The example can be made to have a finite signature by using the Hrushovski-encoding from [32], [33]: the encoding is a structure B with a finite relational signature such that Pol(B) satisfies every pseudo-variant of any minor condition that is satisfied in Pol(A) by injections [32,Proposition 3.16], in particular the pseudo-Siggers condition. On the other hand, there exists a pp-interpretation of A in B by [32,Proposition 3.13] combined with [31], which yields the absence of pseudo-WNU operations in Pol(B). The structure B still has slow orbit growth [32,Proposition 3.12].…”
Section: Countably Categorical Structures Without Pseudo-wnu Polymorp...mentioning
confidence: 99%
See 1 more Smart Citation
“…The example can be made to have a finite signature by using the Hrushovski-encoding from [32], [33]: the encoding is a structure B with a finite relational signature such that Pol(B) satisfies every pseudo-variant of any minor condition that is satisfied in Pol(A) by injections [32,Proposition 3.16], in particular the pseudo-Siggers condition. On the other hand, there exists a pp-interpretation of A in B by [32,Proposition 3.13] combined with [31], which yields the absence of pseudo-WNU operations in Pol(B). The structure B still has slow orbit growth [32,Proposition 3.12].…”
Section: Countably Categorical Structures Without Pseudo-wnu Polymorp...mentioning
confidence: 99%
“…On the other hand, there exists a pp-interpretation of A in B by [32,Proposition 3.13] combined with [31], which yields the absence of pseudo-WNU operations in Pol(B). The structure B still has slow orbit growth [32,Proposition 3.12]. Since the structure A is a homogeneous model-complete core, its encoding B can be made so that it is a model-complete core as well: being homogeneous itself A need not be homogenized for the encoding, and the new relations used in the encoding can be enriched by relations for their complement (the proof of SAP in [32,Lemma 3.5] still works).…”
Section: Countably Categorical Structures Without Pseudo-wnu Polymorp...mentioning
confidence: 99%
“…A similar characterization exists for bounded width via wnu identities of all arities ≥ 3 [6] and some other identities [41]. For templates within the range of Conjecture 1.6, it is believed that membership in P can be described by the local (i.e., on all finite subsets of the domain) satisfaction of non-trivial nonnested identities [3], [4], [7], [35], [36], since this condition obstructs the most obvious reason for NP-hardness, namely the pp-construction of an NP-hard finite template. The condition implies the global satisfaction of the (slightly nested) pseudo-Siggers identity e•s(x, y, x, z, y, z) = f •s(y, x, z, x, z, y) [8], [9].…”
Section: A the First Dilemma Of The Infinite Sheepmentioning
confidence: 99%
“…While ω-categoricity guarantees the availability of certain algebraic methods to investigate the mathematical structure of the template, it turns out that contrary to the finite-domain case the structure as measured by these methods is, without further assumptions, largely insufficient to make predictions about the computational complexity of the CSP [13], [35], [36]. In particular, even if the "solution space" (i.e., all orbits of n-tuples) for every given instance I (of length n) is finite, it might not be possible to algorithmically enumerate all orbits of arbitrary length.…”
Section: Introductionmentioning
confidence: 99%
“…This is known to be true also for infinite templates which are ω-categorical, i.e., every instance of the CSP of such instance has only finitely many solutions up to automorphisms [23]. The sole assumption of ω-categoricity is still insufficient to assess the complexity of the CSP [31,32] since the set of possible solutions of any instance up to automorphisms does not need to be algorithmically enumerable. A natural way to achieve this is to additionally require every solution to be described by the relations holding on its image (homogeneity) and that every solution must only be verified locally on subsets of a fixed size (finite boundedness).…”
Section: Introductionmentioning
confidence: 99%